Science

Beaufort wind force scale

The first official use of the ____________ scale was on the voyage of the HMS Beagle in 1831, which was led by Robert FitzRoy, who had been trained by the scale's namesake, Sir Francis Beaufort, a rear admiral in the British Navy. The Beaufort scale is primarily based on wind speed, but also incorporates descriptions of wave height, sea conditions, and land conditions. It starts at 0, corresponding to "calm" winds with a speed less than 1 knot. In most parts of the world, it stops at 12, which is designated "hurricane-force winds." Scores of 2 to 6 are called "breezes," and scores of 7 to 10 are called "gales." Since 1946 the median wind speed for each step has been defined as 1.87 B3/2, where B is the number on the Beaufort scale.

Peduncle

The stem supporting a flower. If multiple flowers bloom from a peduncle, the stems supporting each flower are called pedicels. The torus is the swelling at the top of the pedicel or peduncle, just below the calyx.

William Rowan Hamilton

(1805-1865, Irish) is known for a four-dimensional extension of complex numbers, with six square roots of -1 (±i, ±j, and ±k), called the quaternions.

Robert Millikan

(1868-1953) determined the charge of the electron by meticulously observing oil droplets in an electric field and noting the time it took them to fall a certain distance.

Logarithmic functions, or logarithms,

are functions of the form f(x) = logbx, where b is again a positive number other than 1 (and again called the base). They are the inverses of the exponential functions with the same bases. _________________________ are used to model sensory perception and some phenomena in probability and statistics. The phrase "the logarithm" can refer to a logarithmic function using the base 2 (especially in computer science; this is also called the binary logarithm), e (especially in higher math), or 10 (especially in lower levels of math and physical sciences). The phrase natural logarithm refers to the logarithm base e, and the phrase common logarithm usually refers to the logarithm base 10.

Carbon (C, 6)

is found, by definition, in all organic compounds. It is the fourth most abundant element in the Universe. It has three major isotopes: isotope 12, which is stable; isotope 13, which is used in NMR spectroscopy; and isotope 14, which is radioactive and is the basis of ________ dating. _______'s ability to form four chemical bonds means that it has many different allotropes. The best-characterized natural allotropes are diamond, which consists of a tetrahedral network of carbon atoms, and graphite, which consists of planes of _________ atoms arranged in hexagons. Fullerenes such as buckyballs and _____________ nanotubes, on the other hand, are generally produced synthetically; buckyballs are roughly spherical. More recently, graphene, which is a single layer of atoms shaped like graphite, has proven to have remarkable properties; for example, it is nearly transparent while being about 200 times stronger than an equivalent mass of steel.

The trigonometric functions

represent relations between angles and sides of triangles.

Marie and Pierre Curie

rigorously isolated and experimented on radioactive materials, forming the basis for early nuclear and particle physics.

SM4

was originally cancelled after the Columbia Disaster by then-NASA Administrator Sean O'Keefe, but was revived by Michael Griffin, who took over the post in 2005. SM4 installed WFC3 (made from some parts of the original WFPC) and the Cosmic Origins Spectrograph (COS), and conducted other repairs. No further repairs are planned, as much of HST's functionality will be replicated with the James Webb Space Telescope, scheduled for launch in 2018.

Pierre de Fermat

(1601-1665, French) is remembered for his contributions to number theory including his little theorem, which states that if p is a prime number and a is any number at all, then ap - a will be divisible by p. He studied [blank] primes, which are prime numbers that can be written as 22n + +1 for some integer n, but is probably most famous for his "last theorem," which he wrote in the margin of Arithmetica by the ancient Greek mathematician Diophantus with a note that "I have discovered a marvelous proof of this theorem that this margin is too small to contain." The theorem states that there is no combination of positive integers x, y, z, and n, with n>2, such that xn + yn = zn, and mathematicians struggled for over 300 years to find a proof until Andrew Wiles completed one in 1995. (It is generally believed that [blank] did not actually have a valid proof.) [blank] and Blaise Pascal corresponded about probability theory.

Isaac Newton

(1643-1727, English) The work of [blank] in pure math includes generalizing the binomial theorem to non-integer exponents, doing the first rigorous manipulation with power series, and creating [blank]'s method for finding roots of differentiable functions. He is best known, however, for a lengthy feud between British and Continental mathematicians over whether he or Gottfried Leibniz invented calculus (whose differential aspect [blank] called the method of fluxions). It is now generally accepted that they both did, independently.

Gottfried Leibniz

(1646-1716, German) is known for his independent invention of calculus and the ensuing priority dispute with Isaac Newton. Most modern calculus notation, including the integral sign and the use of d to indicate a differential, originated with [blank]. He also did work with the binary number system and did fundamental work in establishing boolean algebra and symbolic logic.

Leonhard Euler

(1707-1783, Swiss) is known for his prolific output and the fact that he continued to produce seminal results even after going blind. He invented graph theory by solving the Seven Bridges of Königsberg problem, which asked whether there was a way to travel a particular arrangement of bridges so that you would cross each bridge exactly once. (He proved that it was impsosible to do so.) [blank] introduced the modern notation for e, an irrational number about equal to 2.718, which is now called [blank]'s number in his honor (but don't confuse it for [blank]'s constant, which is different); he also introduced modern notation for i, a square root of -1, and for trigonometric functions. He proved [blank]'s formula, which relates complex numbers and trigonometric functions: ei x = cos x + i sin x, of which a special case is the fact that ei π = -1, which Richard Feynman called "the most beautiful equation in mathematics" because it links four of math's most important constants.

Carl Friedrich Gauss

(1777-1855, German) is considered the "Prince of Mathematicians" for his extraordinary contributions to every major branch of mathematics. His Disquisitiones Arithmeticae systematized number theory and stated the fundamental theorem of arithmetic (every integer greater than 1 has a prime factorization that is unique notwithstanding the order of the factors). In his doctoral dissertation, he proved the fundamental theorem of algebra (every non-constant polynomial has at least one root in the complex numbers), though that proof is not considered rigorous enough for modern standards. He later proved the law of quadratic reciprocity, and the prime number theorem (that the number of primes less than n is is approximately n divided by the natural logarithm of n). [blank] may be most famous for the (possibly apocryphal) story of intuiting the formula for the summation of an arithmetic sequence when his primary-school teacher gave him the task — designed to waste his time — of adding the first 100 positive integers.

Max Planck

(1858-1947) [blank] allowed quantum theory to move forward in the early 20th century by correctly modeling how an object radiates heat, solving the ultraviolet catastrophe, which was a predicted unbounded increase in the amount of radiation emitted at high frequencies. [blank]'s Law of Radiation superseded the Rayleigh-Jeans Law. He suggested that electromagnetic energy could only be emitted in specific packages, called quanta (singular quantum, from the Latin for "how much"), positing that the energy of this photon was equal to its frequency times a fixed value h, now known as [blank]'s constant.

Ernest Rutherford

(1871-1937) [blank]'s gold foil experiment provided the first evidence that each atom is made up of a large, positively-charged nucleus, surrounded by a cloud of negatively-charged electrons. [blank] won the 1908 Nobel Prize in Chemistry for this work. [blank] was also an early leader in nuclear fission techniques, having discovered the decay of carbon-14 and providing the impetus for modern carbon dating. As part of this research, he discovered the proton and neutron, the latter in cooperation with James Chadwick. He is also the only native New Zealander with an element named after him ([blank]ium, atomic number 104).

Albert Einstein

(1879-1955) In one year — 1905, called his annus mirabilis, or "miracle year" — [blank] authored four papers that revolutionized modern physics. The first explained the photoelectric effect in terms of quantized electromagnetic radiation. The second formed the foundation for modern statistical physics by explaining the seemingly-random motion of particles in a fluid, a behavior called Brownian motion. The third reconciled Maxwellian electrodynamics with classical mechanics by positing a finite, constant speed of light, a theory now known as special relativity. The fourth paper contained his statement that the energy of a body is equal to its mass times the speed of light squared (that is, E = mc2). Ten years later, in 1915, [blank] published his theory of general relativity, which generalized special relativity to account for gravitational fields.

Niels Bohr

(1885-1962) [blank] reconciled Rutherford's results from the gold foil experiment with Max Planck's quantum theory to create a model of the atom (the [blank] model) in which electrons resided in specific energy levels at specific stable radii. This model was the basis for Johann Balmer's work with spectroscopy and Johannes Rydberg's energy formula, which explicitly stated the frequency of light that an electron would emit if it went from a higher energy to a lower energy. [blank] and his son fled to the U.S. in World War II under the pseudonym "Baker," and contributed to the Manhattan Project.

Erwin Schrödinger

(1887-1961) [blank] contributed to the early formulations of quantum theory as a foil to Werner Heisenberg, Niels Bohr, and Paul Dirac, criticizing their Copenhagen interpretation of quantum mechanics with thought experiments like his famous [blank]'s Cat argument. He formulated both the time-independent and time-dependent [blank] equations, which are partial differential equations that describe how quantum systems behave. [blank]'s work was the basis for Heisenberg's matrix formalism, Feynman's path-integral formalism, and quantum mechanical perturbation theory, which considers the effects of a small disturbance to a quantum system.

Louis de Broglie (duh-BROH-lee)

(1892-1987) [blank] work quantifying the wave-particle duality of quantum mechanics earned him the 1929 Nobel Prize in Physics. His doctoral thesis, which proposed that all particles have a characteristic wavelength dependent on their momentum, was so groundbreaking that the reviewers passed it directly to Albert Einstein, who endorsed it. In opposition to the probabilistic interpretation of quantum mechanics, [blank] later worked to define a purely causal interpretation, but his work remained unfinished until David Bohm refined it in the 1950s.

Wolfgang Pauli

(1900-1958) [blank] exclusion principle prohibits most types of particles from occupying the same state, and forms the basis for chemical bonds

Enrico Fermi

(1901-1954) [blank] is best known to the public as a main contributor to the Manhattan Project. His work with statistical physics laid the groundwork for modern electronics and solid-state technologies. He applied the Pauli exclusion principle to subatomic particles to create [blank]-Dirac statistics, which accurately predicted the low-temperature behavior of electrons. Particles that obey [blank]-Dirac statistics are called [blank]ons in his honor. [blank] also suggested the existence of the neutrino in order to balance nuclear beta-decay chains.

Werner Heisenberg

(1901-1976) [blank] is most known for his matrix interpretation of quantum theory, which constructs observable quantities as operators that act on a system. His famous uncertainty principle (better translated, however, as "indeterminacy principle") states that the more accurately an object's position can be observed, the less accurately its momentum can. This is because shorter wavelengths of light (used as a sort of measuring-stick) have higher energies, and disrupt a particle's momentum more strongly. [blank] earned the 1932 Nobel Prize in Physics for discovering the allotropic forms of hydrogen.

Paul Dirac

(1902-1984) was one of the first to attempt a generalization of quantum theory to relativistic speeds, the result of which was the [blank] equation.

J. Robert Oppenheimer

(1904-1967) oversaw much of the Manhattan Project, but was later stripped of his security clearance during the McCarthy-era Red Scare, as a result of his acquaintance with communists and his enmity with Edward Teller.

George Gamow

(1904-1968) [blank] was one of the first to explain the implications of the Big Bang theory of cosmology. He correctly predicted the abundance of hydrogen and helium in the early universe, nicknamed Alpher-Bethe-[blank] theory (an intentional pun on the first three letters of the Greek alphabet, alpha, beta, and gamma, for which the otherwise unrelated physicist Hans Bethe was included), and also theorized that the the heat from the Big Bang would still be visible as the cosmic microwave background radiation. Although [blank] received no Nobel for this prediction, the CMB's discoverers, Arno Penzias and Robert Wilson, as well as two later observers, John Mather and George Smoot, did receive Nobels.

Kurt Gödel

(1906-1978, Austrian) was a logician best known for his two incompleteness theorems, which state that if a formal logical system is powerful enough to express ordinary arithmetic, it must contain statements that are true yet unprovable. [blank] developed paranoia late in life and eventually refused to eat because he feared his food had been poisoned; he died of starvation.

Richard Feynman

(1918-1988). [blank] developed a mathematical formalism called the path integral formulation of quantum theory that utilized the "sum over histories," taking into account all possible paths a particle could take. This constituted the creation of quantum electrodynamics and earned him the 1965 Nobel Prize in Physics. He also used the sum over histories in developing [blank] diagrams, which illustrate the interaction of subatomic particles. Aside from being a prolific physicist, [blank] was also an accomplished bongo player and sketch artist.

Andrew Wiles

(1953-present, British) is best known for proving the Taniyama-Shimura conjecture that all rational semi-stable elliptic curves are modular forms. When combined with work already done by other mathematicians, this immediately implied Fermat's last theorem (see above).

Archimedes

(287-212 BC, Syracusan Greek) is best known for his "eureka" moment, in which he realized he could use density considerations to determine the purity of a gold crown; nonetheless, he was the preeminent mathematician of ancient Greece. He found the ratios between the surface areas and volumes of a sphere and a circumscribed cylinder, accurately estimated pi, and developed a calculus-like technique to find the area of a circle, his method of exhaustion.

Murray Gell-Mann

(born 1929) predicted the existence of quarks, which compose protons, neutrons, and other, heavier particles.

Euclid

(c. 300 BC, Alexandrian Greek) is principally known for the Elements, a textbook on geometry and number theory, that has been used for over 2,000 years and which grounds essentially all of what is taught in modern high school geometry classes. The Elements includes five postulates that describe what is now called [blank] space (the usual geometric space we work in); the fifth postulate — also called the parallel postulate — can be broken to create spherical and hyperbolic geometries, which are collectively called non-[blank] geometries. The Elements also includes a proof that there are infinitely many prime numbers.

Area of triangle

1/2 (base)(height)

Surface area of a parallelepiped

2ab+2bc+2ac

Surface area of a sphere

4 x pi x r^2

Volume of a sphere

4/3 x pi x r^3

bijective, or a bijection

A function that is both injective and surjective. If a function is ______________, then it has an inverse. Furthermore, a function can only have an inverse if it is ______________.

Endoplasmic reticulum

A network of tube-like membranes continuous with the nuclear envelope. Part of it are "rough" because they are covered in ribosomes, while other parts are "smooth" because they aren't. In the ________________, proteins undergo modifications and folding to yield the final, functional protein structures.

degree 0.

A polynomial that is just a constant

linear

A polynomial with degree 1, like 3x,

Cnidaria

Also called Coelenterata see-LEN-tur-AH-tuh, theydevelop from a diploblastic (two-layered) embryo, and have two separate tissue layers and radial body symmetry. Many have two life stages, the mobile, usually bell-like medusa and the sessile polyp. All have nematocysts, or stinging cells, for capturing prey, and some can inflict painful stings on swimmers. Examples include the hydras, sea anemones, corals, jellyfishes, and Portuguese man-o-war (which is actually an aggregation of colonial cnidarians).

Mollusca

Are second in diversity only to the arthropods. Body plans within this phylum are diverse, but general characteristics include a soft body covered by a thin mantle, with a muscular foot and an internal visceral mass. There are two fluid-filled body cavities derived from mesodermal tissue: a small coelom and a large hemocoel that functions as an open circulatory system. Many ___________ have a shell composed of calcium carbonate and proteins, secreted by the mantle. Familiar groups within the ______________ include the classes Gastropoda (slugs, snails), Bivalvia (clams, oysters, scallops), and Cephalopoda (nautilus, squids, octopi).

Annelida

Are segmented worms and represent the first lineage of truly eucoelomate (having a body cavity lined with mesoderm-derived tissue) animals; their body cavities are lined with tissue derived from the embryonic mesoderm. ___________ classes include the marine Polychaeta, as well as the mostly terrestrial Oligochaeta (including the earthworms, Lumbricus) and the mostly aquatic Hirudinea, or leeches. Characteristics of ________________ include nephridia (kidney-like structures), blood vessels, and, in some classes, hermaphroditism.

Phobos

Both ___________ ("fear") and Mars' smaller moon Deimos ("dread") were discovered by Asaph Hall III in 1877. At just 3,700 miles above the Martian surface, ___________ orbits more closely to its planet than any other moon in the Solar System. Because it orbits Mars faster than Mars rotates, each day it appears (from the Martian surface) to set twice in the east. Geological features on ___________ , including the Stickney Crater, are primarily named for either astronomers (Stickney was the maiden name of Asaph Hall's wife) or characters from Jonathan Swift's Gulliver's Travels. In 1971 the U.S.'s Mariner IX became the first spacecraft to provide close-up photos of Phobos.

Echinodermata

Characteristics of this phylum include an endoskeleton composed of many ossicles of calcium and magnesium carbonate, a water vascular system, a ring canal around the esophagus, and locomotion by tube feet connected to the water vascular system. Unique to ______________ is the five-fold radial symmetry obvious in sea stars (starfish), sea urchins, and sea lilies. Others, like sea cucumbers, have varying degrees of bilateral symmetry. In the ______________ body plan, a true head is absent; the anatomical terms oral (mouth-bearing) and aboral (away from the mouth) are used to describe orientation of the body surfaces. Feeding adaptations include particle feeding through the water vascular system, everting the stomach to engulf prey (sea stars), and a scraping device called Aristotle's lantern (sea urchins).

Calculus operations

Derivative, integral, slope at a point, local extrema, points of inflection, and critical points

Permutations

EX: Suppose we want to find the number of ways to arrange the three letters in the word CAT in different two-letter groups where CA is different from AC and there are no repeated letters. - is known as 3_P_2, which is 3!/(3-2)!

Vacuoles

Found mainly in plants and protists, _____________ are liquid-filled cavities enclosed by a single membrane. They serve as storage bins for food and waste products. Contractile ___________ are important for freshwater protists to rid their cells of excess water that accumulates because of salt imbalance with the environment.

Chloroplasts

Found only in plants and certain protists, the _______________ contains the green pigment chlorophyll and is the site of photosynthesis. Like the mitochondrion, a _____________ is a double-membrane-bound organelle, and it has its own DNA and ribosomes in the stroma. ______________ contain grana, which are stacks of single membrane structures called thylakoids on which the reactions of photosynthesis occur.

Mohs scale

Invented by Friedrich Mohs in 1812, the ________ scale is based on the abilities of minerals to scratch one another. The original scale assigned a value of 1 to talc, which can be scratched by essentially every solid known, and a value of 10 to diamond, which (among naturally occurring minerals) can only be scratched by other diamonds. The steps are of arbitrary size, with a 1-point difference corresponding to anywhere from a 1.5-fold to a 4-fold increase in hardness; diamond is about 1600 times harder than talc. Following the discovery of more ultra-hard minerals, scientists have proposed extending the scale so that diamond is 15 instead of 10.)

Monocots vs. dicots

Most (but not all) angiosperms fall into one of two classes based on the number of cotyledons, or embryonic seed-leaves, in the plant embryo. Monocots, or Monocotyledonae, have one cotyledon, while dicots, or Dicotyledonae, have two. While there are no other hard-and-fast distinguishing characteristics between the two groups, plants in each category tend to share other characteristics: Monocots produce pollen grains that have a single furrow (monosulcate); flower parts in multiples of three; numerous, fibrous roots; parallel leaf veins; and stems with scattered vascular bundles. They also lack secondary growth, remaining herbaceous throughout their lives. Dicots, on the other hand, tend to have pollen with three furrows (tricolpate); flower parts in multiples of four or greater; taproot systems; stems with rings of vascular tissue; and branching leaf veins. Many of them exhibit secondary growth that produces wood.

Bryophytes vs. pterophytes

Not all plants produce seeds. Seedless plants are divided into bryophytes (mosses, liverworts, and hornworts) and pterophytes (ferns, club mosses, quillworts, and horsetails). Both of these groups, like all other plants, reproduce by producing sperm and eggs on a structure called the gametophyte. The gametes fuse to form another structure called the sporophyte, which produces spores that disperse and grow into new gametophytes. Both groups produce flagellated sperm that require water for fertilization. Note that these uses of "bryophyte" and "pterophyte" here are informal, and should not be confused with the actual phyla Bryophyta (true mosses) and Pteridophyta (true ferns). Bryophytes are small enough that water and nutrients can diffuse to all parts of the plant without any specialized vascular tissue. They lack true leaves and roots, instead fastening themselves to the ground with rhizoids. Unlike other land plants, bryophytes have a prominent gametophyte stage that is usually dioicous, meaning that an individual plant produces only one type of gamete (either sperm or egg). The short-lived sporophyte grows from the female gametophyte. The more complex pterophytes can grow taller thanks to vascular tissues (see number 4 below) that provide structural support and transport water and other materials throughout the plant. Many of them do have true leaves and roots. Pterophytes have a prominent sporophyte stage that grows from a small, short-lived gametophyte. Pterophyte gametophytes may be dioicous or monoicous, producing both sperm and egg on the same plant.

Centrioles

Not found in plant cells, _____________ are paired organelles with nine sets of microtubule triplets in cross section. They are important in organizing the microtubule spindle needed to move the chromosomes during mitosis.

Deimos

One-seventh the mass of Phobos and further away from the Martian surface, Deimos was found by Asaph Hall at the U.S. Naval Observatory six days before he discovered Phobos. Its largest and only named craters are Swift and Voltaire; Deimos's surface doesn't appear as rough as Phobos's because regolith has filled in some of the craters. A still-controversial and unproven hypothesis holds that Deimos (and possibly Phobos as well) were asteroids perturbed out of their orbit by Jupiter and then captured by the gravity of Mars.

the zero function, f(x) = 0

Only one function is both even and odd

Iapetus

Saturn's third-largest moon after Titan and Rhea and, like Rhea, was discovered by Giovanni Cassini in 1671. It was named based upon a suggestion from John Herschel (son of the discoverer of Uranus, William Herschel) for the Titans of Greek mythology, the brothers and sisters of Cronos (Saturn). Iapetus has a distinctive two-tone coloration; part of it is red-brown, while part is bright gray. Features on Iapetus are named for people and places from the French Song of Roland, including Charlemagne Crater and the bright northern region Roncevaux Terra. In 2004 the Cassini orbiter found an equatorial ridge running over 800 miles long and 10 miles wide that gives Iapetus some of the highest peaks in the solar system; its existence has not yet been explained.

Angiosperms vs. gymnosperms

Seed-producing plants can be divided into gymnosperms (cycads, ginkgos, conifers, and gnetophytes) and angiosperms (phylum Anthophyta, or flowering plants). Most of these plants produce male gametophytes that grow into the female, allowing fertilization to take place in relatively dry conditions. Many of them also exhibit secondary growth of woody tissues, allowing them to grow even taller than the pterophytes. The word gymnosperm means "naked seed," referring to the fact that their gametophytes develop on the surface of leaves or on the scales of cones. In contrast, angiosperm means "receptacle seed." Their gametophytes develop enclosed within flowers. Angiosperms are further classified based on their seed structure, described below.

Pythagorean triples

Sets of small integers that satisfy the equation of the Pythagorean theorem, a^2 + b^2 = c^2, and could therefore be the side lengths of a right triangle. The simplest ones are {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, and {8, 15, 17}.

Galois gal-wah theory

That impossibility is the topic that began an area of study, which is part of abstract algebra.

Nucleus

The "command central" of the cell because it contains almost all of the cell's DNA, which encodes the information needed to make all the proteins that the cell uses. The DNA appears as chromatin through most of the cell cycle, but condenses to form chromosomes when the cell is undergoing mitosis. Within the ___________ there are dense bodies called nucleoli, which contain ribosomal RNA. In eukaryotes, the _____________ is surrounded by a selectively-permeable nuclear envelope.

pH scale

The ____ scale, developed by S. P. L. Sørensen in 1909, is used to quantify acidity. The pH (power of hydrogen) of a solution is defined as the opposite of the (base-10) logarithm of the concentration of protons in a solution: pH = -log10[H+]. (The brackets are standard notation in chemistry for "the concentration of.") Thus, greater concentrations of protons correspond to smaller pH values. At 25°C, the neutral (neither acidic nor basic) pH is 7; solutions with a pH less than 7 are considered acidic, and solutions with a pH greater than 7 are considered basic.

Saffir-Simpson scale

The _______-____________ scale is a measure of wind speed and damage from hurricanes. It was developed in 1971 by Herbert Saffir, a civil engineer, and Robert Simpson, then the director of the National Hurricane Center. It rates hurricanes on a 1-to-5 scale: a 1 corresponds to a wind speed of 74 to 95 miles per hour, which causes "some damage." A 5 causes "catastrophic damage," with wind speeds over 157 miles per hour and affected areas uninhabitable for weeks or months.

Richter scale

The __________ scale measures earthquake intensity. Developed by Caltech professor Charles Francis Richter, it measures the shaking intensity associated with earthquakes, as quantified by the amplitude of vibrations on a seismograph. A magnitude-5.0 earthquake will have an amplitude 10 times larger than that of a magnitude 4.0 quake. The energy associated with an earthquake is actually proportional to the 3/2 power of the magnitude: a 1-point difference on the Richter scale corresponds to a 103/2-fold (about 31.6) difference in energy. Because of difficulties in measuring the magnitudes of large earthquakes, the Richter scale has been superseded by the moment magnitude scale, which uses a different formula but retains the logarithmic nature (and correlates to measurements on the Richter scale).

Pauling scale

The __________ scale, devised by Linus Pauling in 1932, is one of several scales that measure electronegativity, the extent to which atoms attract electrons in chemical bonds. Higher values correspond to stronger attractions. Francium has the lowest value, about 0.7, while fluorine has the highest value, about 4.0. (Noble gases are not assigned values on the Pauling scale, since they were not known to form any bonds when Pauling devised it.) Differences in electronegativity characterize bonds: the greater the difference, the more ionic the bond.

Decibel scale

The ___________ scale can describe any kind of power, but is most commonly used to describe the intensity of sound waves. The decibel (abbreviated dB) is one tenth of a larger unit, the bel (abbreviated B), named after inventor Alexander Graham Bell. The intensity of a sound in decibels is given by the formula I = 10 log(P1/P0), where P1 is the intensity of the sound being measured (in watts per square meter) and P0 is a reference intensity, which is based on the least powerful sound wave that can be detected by the average human ear (namely 10-12 W/m2). A 10-dB increase in sound intensity corresponds to multiplying the energy of the sound wave by 10. A normal conversation has a volume of about 70 dB.

Similar figure

The areas are related by the square of any corresponding length, and the volumes are related by the cube of any corresponding length. For instance, if a square has a diagonal that is 30% longer than another square, it has an area that is 1.30 × 1.30 = 1.69 times as great (69% greater). Similar reasoning applies to perimeters, side lengths, diameters, and so forth.

Platyhelminthes

The flatworms are the most primitive phylum to develop from a triploblastic (three-layered) embryo. They have bilateral body symmetry, and are acoelomate (lacking a true body cavity), so that the space between the digestive tract and the body wall is filled with tissue. As the name implies, they are generally flat-bodied. They have a true head and brain, but the digestive system has only one opening, which functions as both mouth and anus. Most are hermaphroditic. This phylum includes parasites such as the tapeworms and flukes, as well as free-living (i.e., non-parasitic) organisms such as the planarians.

Triton

The largest moon of Neptune and the only large moon with a retrograde orbit (that is, an orbit opposite to the rotation of its planet), Triton is the seventh-largest moon in the solar system and is thought to have been captured from the Kuiper Belt. For over 100 years after its 1846 discovery, Triton was thought to be Neptune's only moon; Nereid wasn't discovered until 1949. (There are thirteen known satellites now.) Triton is geologically active and has geysers that are assumed to erupt nitrogen. Because of the activity, impact craters on Triton are relatively scarce; most of the larger craters were formed by volcanic activity. Triton orbits around Neptune in almost a perfect circle. Voyager 2 visited Triton in 1989 and is the only space probe to have done so (and no more are currently planned). Much of Triton's western hemisphere consists of an unexplained series of fissures and depressions sometimes called "cantaloupe terrain." Triton's features are named after various water spirits, monsters, and sacred waters from mythology.

Charon

The largest satellite of the dwarf planet Pluto, Charon wasn't discovered until 1978. (As of 2013, Pluto has five known moons, the last two discovered in 2011 and 2012.) Unlike Pluto, which is covered with nitrogen and methane ices, Charon appears to be covered in water ice and may also have active cryo-geysers. Because the center of mass of the Pluto-Charon system lies outside of either one, Charon doesn't truly orbit Pluto; when Pluto was reclassified as a dwarf planet in 2006, an argument was made (but not accepted) to classify Pluto-Charon as a binary system. The IAU still considers Charon, which is roughly half the size but has only 11% the mass of Pluto, to be a satellite. The New Horizons mission visited Charon and Pluto in 2015. Charon was named by its discoverer, James Christy of the Flagstaff Naval Observatory; the IAU approved the name in 1985. Internationally Charon is pronounced like the Greek mythological figure, "CARE-on", but Christy's choice of name was inspired by his wife Charlene, so NASA and New Horizons personnel use "SHARE-on".

Ribosomes

The machines that coordinate protein synthesis, or translation. They consist of several RNA and protein molecules arranged into two subunits. ________________ read the messenger RNA copy of the DNA and assemble the appropriate amino acids into protein chains.

Earth's moon

The moon, also called Luna, is the fifth-largest satellite in the solar system, the largest relative to the size of the planet it orbits, and the second densest. The USSR's Luna unmanned spacecraft first reached the moon in 1959, and Apollo 8 became the first manned mission to orbit the moon, in 1968. The 1967 Outer Space Treaty guarantees the rights of all nations to explore the moon for peaceful purposes. The flat dark lunar plains are called maria (singular: mare) and are mainly concentrated on the near side of the moon. The most famous one is Mare Tranquillitatis, the Sea of Tranquility, where Apollo 11 first landed on the moon in 1969. The Apollo program landed on the moon five more times.

Arthropoda

The most diverse and successful animal phylum on earth (incorporating about 75% of all described animal species), the ______________ are characterized by jointed legs and a chitinous exoskeleton. Like annelids, they are segmented, but unlike annelids, their segments are usually fused into larger body parts with specialized functions (such as the head, thorax, and abdomen of an insect). _____________ are often divided into four subphyla: Uniramia (insects, centipedes, millipedes); Chelicerata (arachnids, sea spiders, horseshoe crabs); Crustacea (shrimps, lobsters, crabs, crayfish, barnacles, pillbugs), and Trilobitomorpha (the trilobites, now extinct).

coefficient.

The number at the beginning of each term

Chordata

The phylum that contains humans, ___________ is divided into three subphyla: Urochordata, the sea squirts; Cephalochordata, the lancelets, and Vertebrata, the true vertebrates, which is the most diverse subphylum. Defining traits of ___________ include pharyngeal gill slits, a notochord, a post-anal tail, and a dorsal hollow nerve cord. In vertebrates, some of these structures are found only in embryonic stages. The lancelet Amphioxus (Branchiostoma) is often used as a demonstration organism in biology labs.

Stamen

The pollen-producing reproductive organ of the flower. The stamen consists of a thin filament topped by an anther, which actually contains the pollen.

Mitochondria

The powerhouses of the cell. _______________ are double-membrane-bound organelles that are the site of respiration and oxidative phosphorylation, processes that produce energy for the cell in the form of ATP. The inner membrane of a _______________ forms folds called cristae, which are suspended in a fluid called the matrix. The mitochondrial matrix contains DNA and ribosomes.

Nematoda

The roundworms are unsegmented worms that live in a variety of habitats. They are pseudocoelomate; the three tissue layers are concentric, but the body cavity is not lined with tissue derived from the mesoderm (middle embryonic layer). They include both free-living and parasitic species; human parasites include hookworms and the causative agents of elephantiasis, trichinosis, and river blindness. Soil _____________ may be crop pests, while others are beneficial predators on other plant pests. The _______________ species Caenorhabdis elegans is a common subject in genetics and developmental-biology labs.

Temperature scales

The scales most frequently used to measure temperatures in science are the Kelvin and Celsius scales. The Celsius scale, developed by Swedish scientist Anders Celsius in the early 1700s, assigns a value of 0°C to the freezing point of water (at a pressure of 1 atmosphere), and 100°C to the boiling point of water (at the same pressure). The Kelvin scale is based on the triple point of water, the point at which water's solid, liquid, and gaseous phases can coexist in equilibrium: 1 K is defined as 1/273.16 of the temperature of water at its triple point. Kelvins are treated like all other SI units: a temperature of 100 K is read as "one hundred kelvins," not "one hundred degrees kelvin." Differences on the Celsius scale have the same magnitude as differences on the Kelvin scale: a gap of 1°C between temperatures is the same as a gap of 1 K. Therefore the lowest possible temperature, absolute zero (0 K) is equal to -273.15°C, and (at a pressure of 1 atmosphere) water freezes at 273.15 K and boils at 373.15 K.

Porifera

The sponges are all water-dwellers (98% marine, 2% freshwater), and are sometimes classified separately from other animals because of their asymmetric bodies and lack of distinct tissues. They are sessile (immobile) except in early dispersing stages, and collect food particles via the sweeping motions of flagellated cells called choanocytes

Golgi apparatus

The stack of flattened, folded membranes that forms the Golgi apparatus acts as the "post office of the cell." Here proteins from the ribosomes are stored, chemically modified, "addressed" with carbohydrate tags, and packaged in vesicles for delivery.

Xylem vs. phloem

There are two types of vascular tissue in plants. Xylem transports water and soluble nutrients from the roots to the leaves. Phloem, on the other hand, carries nutrients like sucrose from their origin of synthesis or absorption to all parts of the plant. Both tissues originate in the procambium of the apical meristems of both the stems and roots. In woody plants, secondary vascular tissues arise in the vascular cambium. Xylem contains distinct elongated cells called tracheids that have lignified cell walls and help provide structural support. Vessel elements are also reinforced by lignin, but they are open at each end at perforation plates and connect to form long tubes for water transport. Xylem functions via transpirational pull and osmosis. Cell types in phloem include companion cells, fibers, and sclereids. In trees, it is usually the innermost layer of the bark.

Fujita-Pearson and Enhanced Fujita scales

These scales measure tornado strength. The _______-___________ scale was introduced in 1971 by Ted _______, a meteorology professor at the University of Chicago, and Allen Pearson, director of what is now the Storm Prediction Center. The original scale went from F0 (wind speeds lower than hurricane force, which should cause little to no damage) to F5 (wind speeds of 260 miles per hour, which should cause "incredible damage"). _______ also included an "inconceivable damage" category for tornados exceeding 319 miles per hour (theoretically possible, but no such tornado has ever been observed). In 2007 the Enhanced Fujita (EF) scale was introduced, narrowing the speed ranges for each category: an EF5 begins at "just" 200 miles per hour.

Titania and Oberon

Uranus's largest moons, Titania and Oberon, are named for characters from Shakespeare's A Midsummer Night's Dream. (Other Uranian moons are named for characters from either Shakespeare or Alexander Pope.) They were discovered on the same day in 1787 by William Herschel, who also discovered Uranus itself in 1781. In 1986 Voyager 2 became the only spacecraft to date to visit the Uranian moons. Because Uranus orbits the sun almost on its side and Titania and Oberon orbit Uranus in the same plane as its equator, the moons have extreme seasons: Titania's poles spend over 42 years in nonstop sunlight followed by 42 years of darkness. Most of Titania's features are named for settings or female characters from Shakespeare — its largest crater is Gertrude Crater, after Hamlet's mother — while most of Oberon's are named after settings or male characters from Shakespeare. However, Oberon's largest feature is Mommur Chasma, which is named from a French epic poem.

Combinations

When we want to find the number of combinations of size 2 without repeated letters that can be made from the three letters in the word CAT, order doesn't matter; We say '3 choose 2' and write 3_C_2. 3_C_2 = 3_P_2/2!

Mach number

_______ numbers measure speed. Based on a suggestion by Swiss aeronautical engineer Jakob Ackeret, it was named after Ernst Mach, an Austrian physicist who studied — among other things — the Doppler effect, sensory perception, and the origin of inertia. The Mach number is defined as the ratio of the speed of an object to the speed of sound in the same medium. So an object moving at the speed of sound (which in dry air at 20°C is about 343 m/s) has a speed of Mach 1, and an object moving at twice the speed of sound has a speed of Mach 2.

Cilia and flagella

___________ and ____________ are important organelles of motility, that is, they allow the cell to move. _____________ are long, whip-like structures, while ______________ are short, hair-like projections. Both contain a 9 + 2 arrangement of microtubules in cross-section (two microtubules in the middle, nine pairs in a circle around the outside) and are powered by molecular motors of kinesin and dynein molecules.

Lysosomes

______________ are membrane-bound organelles that contain digestive enzymes that break down proteins, lipids, carbohydrates, and nucleic acids. They are important in processing the contents of vesicles taken in from outside the cell. It is crucial to maintain the integrity of the ________________ membranes because the enzymes they contain can digest cellular components as well.

Theodore von Kármán

a fluid dynamicist by training. As a graduate student at Göttingen, he described the so-called Kármán vortex street (a form of turbulence in flow going past a cylinder, which is responsible for driving the vibration or "singing" of power lines) and went on to provide the theoretical basis for the idea of turbulent flows. He contributed to the construction of the wind tunnel at the Guggenheim Aeronautical Laboratory, which eventually became the Jet Propulsion Laboratory. He also formed the company Aerojet to develop short-takeoff aircraft technologies. The Kármán line is the accepted boundary between the Earth's atmosphere and outer space, and the Kármán ogive is the shape of the cone of rockets curving into the main body, which minimizes drag during rocket burn.

period

a function of one variable f is periodic if f(x+p) = f(x) for every x in the domain of the function and some positive number p because the graph repeats itself every p units. While the trigonometric functions are the periodic functions most commonly encountered by high school math students, some other functions like triangle waves are also periodic; in general, functions representing waves tend to be periodic.

quadratic

a polynomial with degree 2, like 3x2 - 8x + 4

cubic

a polynomial with degree 3

monomial

a polynomial with one term, like 2x or -12x2

trinomial

a polynomial with three terms

binomial

a polynomial with two terms

Gene Kranz

a trained aeronautical engineer and pilot, he is best known for his Flight Directorship during the Mercury and Apollo projects. He presided over a departure from NASA's traditional incremental testing structure, in favor of a more aggressive, manned campaign ("all-up testing"). As part of the Apollo 13 "white team," Kranz and his associates engineered the free-return trajectory and human-factors management that brought the Apollo 13 crew back safely after a near-fatal spacecraft anomaly.

Volume of a parallelepiped

abc

Hubble Space Telescope Servicing Missions (SM1, SM2, SM3A, SM3B, and SM4)

all utilized spacewalks staged from a Space Shuttle.

Differentiable functions,

also studied in calculus, are functions for which the derivative can be found (because a particular limit, called a difference quotient, exists). Every ___________________________--- is continuous, but some continuous functions are not differentiable; mathematicians thus say that ____________________ is a stronger property than continuity. In terms of graphs, a _____________________ has a "smooth" graph with no corners or cusps (and also, because continuity is required, no holes, jumps, or asymptotes). All polynomials are ___________ as are the sine and cosine functions, and exponential and logarithmic functions. However, the absolute value function f(x) = |x| is not ________________ because it has a "corner" at x = 0 (but recall that it is still continuous).

Robert Goddard

an early explorer of the theory and practice of launching rockets. His work provided the foundation for modern rocketry: in particular, gimballed engines (engines where the exhaust nozzles can change direction allowing the rocket to be steered), fuel pumps, steering with vanes, and gyroscopic stabilization. His seminal monograph on the subject was 1919's A Method of Reaching Extreme Altitudes. The next year, he put forward a concept for a rocket launch to the moon that was widely ridiculed in the press as being unrealistic. Goddard is the namesake of the NASA Goddard Spaceflight Center in Maryland.

Partons

an older name that was used for the "internal parts" of hadrons before the discovery and widespread acceptance of the quark model. Models based on [blank] are still used but, for the most part, it was determined that [blank] were quarks and the term is rarely used at the high school level except in historical contexts.

Quarks

another class of fundamental particle. They also come in six flavors: up, down, charm, strange, top (occasionally called "truth"), and bottom (occasionally "beauty"). The up, charm, and top [blank] have a charge of +2/3, while the down, strange, and bottom have a charge of -1/3. All [blank] are fermions, and they combine in pairs to form mesons and in triples to form baryons. The enormous mass of the top [blank] (178 GeV) made it difficult to create in particle accelerators, but its discovery in 1995 confirmed an essential element of the Standard Model of particle physics. The name "[blank]" comes from the line "Three [blank] for Muster Mark" in Finnegans Wake that appealed to Murray Gell-Mann. The study of [blank] (and of the strong nuclear force) is quantum chromodynamics.

Hadrons

any particles made out of quarks (alternatively, any particle affected by the strong nuclear force). Generally, this means the baryons and the mesons. All [blank] are colorless (in the sense of the combined color of their constituent quarks). The name "[blank]" comes from the Greek for "thick."

Polynomials

are functions made of terms added together, in which each term is a number times a product of variables raised to nonnegative-integer powers. For instance, 3x2y and -πx7y2z3 are each terms, so 3x2y - πx7y2z3 is a polynomial. (Individual terms are also considered polynomials.) Much of math is concerned with polynomials involving only one variable, such as -x3 + 2x2.

Surjective functions, or surjections,

are functions that achieve every possible output. For instance, if you are thinking of functions whose domain and codomain are both the set of all real numbers, then f(x) = tan(x) is surjective, because every real number is an output for some input. But f(x) = x2 is not surjective, because (for instance) -3 is not an output for any real-number input. The term image is sometimes used for the set of all output values that a function actually achieves; a surjective function, then, is one whose image equals its codomain.

Injective functions, or injections

are functions that do not repeat any outputs. For instance, f(x) = 2x is injective, because for every possible output value, there is only one input that will result in that output. On the other hand, f(x) = sin(x) is not injective, because (for instance) the output 0 can be obtained from several different inputs (0, π, 2π, and so on). If you have the graph of a function, you can determine whether the function is injective by applying the horizontal line test: if no horizontal line would ever intersect the graph twice, the function is injective.

Quadratics

are polynomials of degree 2. The graph of a quadratic equation will be in the shape of a parabola that opens straight up (if the coefficient on the x2 term is positive) or straight down (if that coefficient is negative). It is possible to find the roots of a quadratic by graphing it, factoring it, completing the square on it, or using the quadratic formula (itself derived by completing the square) on it. If the quadratic is in the form ax2 + bx + c, then the expression b2 - 4ac, which appears in the quadratic formula, is called the discriminant. If the discriminant is positive, the quadratic will have two real roots; if the discriminant is zero, the quadratic will have one real root (said to have a multiplicity of 2); and if the discriminant is negative, the quadratic will have two non-real complex roots (and if the coefficients of the quadratic are real numbers, the complex roots will be conjugates of each other).

Exponential functions

are those of the form f(x) = bx, where b (called the base) is a positive number other than 1. ____________________ are used to model unrestricted growth (such as compound interest, and animal populations with unlimited food and no predators) and decay (such as radioactive decay). The phrase "the ____________________________" refers to the function f(x) = ex, where e is a specific irrational number called Euler's number, about equal to 2.718. ________________________________ have the interesting property that their derivatives are proportional to themselves.

Periodic functions

are those whose graph repeats a pattern (specifically, the graph has translational symmetry).

STS-51-L and STS-107 (the Challenger and Columbia accidents respectively)

are two Space Shuttle (or Space Transportation System) launches known mostly for their accidents and subsequent losses of life. The Challenger disaster was attributed by the Rogers Commission (the investigative body set up after the accident) to poor performance of the solid rocket booster (SRB) O-rings. The O-rings lost integrity and became brittle at low temperatures, such as those present on the morning of the launch. The failure of the O-rings caused "blow-by," where hot gasses escaped the booster joint, ultimately resulting in the destruction of Challenger. The Rogers Commission also cited both NASA and SRB contractor Morton Thiokol for a failure to redesign the SRB joint, known to be dangerous—manifestations of "go fever." According to the Columbia Accident Investigation Board, the disaster on STS-107 was due to a piece of foam from the external fuel tank hitting and breaching the left wing of the Orbiter during launch. The breach damaged the heat shielding, allowing hot gas to enter the Orbiter during re-entry. Ultimately, that damage caused the vehicle to disintegrate over Texas. Both missions resulted in the complete loss of crew (seven crew were on each mission) and orbiters. Both modes of failure had been previously observed in earlier missions, but went un-fixed because those missions were successful.

Wernher von Braun

at one time a student of Oberth in the Spaceflight Society. Von Braun is best-known for leading Nazi Germany's development and construction of the V-2 rocket (literally, "vengeance weapon"), which wreaked destruction on southern England during World War II. After World War II, he was recruited to the US as part of Operation Paperclip, and proposed to launch a space station carrying a nuclear arsenal (though he hedged the concept as "particularly dreadful"). He presided over Mercury-Redstone development as Director of NASA's newly-opened Marshall Spaceflight Center, which produced the rockets used in the Mercury spaceflights, and the Saturn V rocket used to launch the Apollo spacecraft.

The Hershey-Chase experiment (1952)

by Alfred Hershey and Martha Chase, demonstrated that the material responsible for inheritance of traits was DNA rather than protein. The experiment was carried out by creating radiolabeled T2 bacteriophages (viruses that infect bacteria). In one population, the phages' DNA contained phosphorus-32 in its backbone; in the other population, the phages' proteins contained sulfur-35. The phages were then allowed to infect E. coli. After using a centrifuge to remove the viral coats from the bacteria, Hershey and Chase found that the viruses labeled with sulfur did not transfer their radioactivity to the cells, while the viruses labeled with phosphorus did. This result, combined with other experiments, demonstrated that the genetic material was DNA, not protein.

Calyx

composed of sepals, specialized green leaves that protect the flower as a bud and provide support for the fully bloomed flower

Baryons

composite (i.e., non-fundamental) particles made from three quarks. The most common examples are the proton (two up quarks and one down quark) and the neutron (two down quarks and one up). All [blank] are fermions. Quarks possess a characteristic called "color" (which has nothing to do with visual color) which can be either red, green, or blue (arbitrary names; again, no relation to the colors we see). A [blank] must have one quark of each color so that the "total color" (analogous to mixing red, green, and blue light) is colorless (i.e., "white"). The word "[blank]" comes from the Greek for "heavy." The total number of [blank] is conserved (again, counting anti-[blank] as -1).

Mesons

composite particles generally made from a quark and an anti-quark. There are dozens of examples including the pion, kaon, J/Psi, Rho, and D. All [blank] are bosons. The quark and anti-quark must have the same color (such as red and anti-red) so that the resulting [blank] is colorless (or "white"). It is also possible to make [blank] out of two (or more) quarks and the same number of anti-quarks, but this kind of particle (a "tetraquark") is rare, both in nature and in quiz bowl.

The Michelson-Morley experiment (1887)

conducted by Albert Michelson and Edward Morley at what is now Case Western Reserve University, disproved the existence of the luminiferous aether, a hypothetical medium through which light waves supposedly moved. (The aether is sometimes called simply "ether," but is not to be confused with ethers from organic chemistry.) The experiment used an interferometer, a device that splits a beam of light and aims it using mirrors to allow the beam to interfere with itself; the interferometer was mounted on a slab of marble floating in a pool of mercury so that it could turn without friction, to eliminate the possibility that the interferometer was misoriented. While Michelson and Morley expected to find a shift in the interference pattern's fringes as a result of the ether, the experiment showed that the Earth had no motion relative to the ether, suggesting that the ether did not exist. Often called the most famous failed experiment in science, the Michelson-Morley experiment is a fundamental test of special relativity.

The Stern-Gerlach experiment (1922)

conducted by Otto Stern and Walther Gerlach, demonstrated that the angular momentum of an atom is quantized. A beam of silver atoms was fired through an inhomogeneous magnetic field (one that varies through space). Instead of hitting a screen in a continuous distribution, they hit at discrete points, demonstrating the quantized nature of angular momentum. This experiment was actually performed several years before the concept of electron spin was even proposed. A variant on this experiment was used to create an energy source for the first hydrogen maser.

Rational functions

consist of one polynomial divided by another polynomial. The denominator polynomial cannot be the zero polynomial, because dividing by zero is undefined. Examples therefore include 1/x, x2/(x - 3), and (x2 + 1)/(x2 - 1). Every polynomial can be considered to be a rational function because 1 is a polynomial and dividing by 1 doesn't change an expression (so to consider the polynomial x3 as a rational function, think of it as x3/1).

SM1

corrected Hubble's flawed optics by installing COSTAR (a corrective optics system), while removing the High-Speed Photometer to make room. It also replaced the original Wide Field and Planetary Camera, or WFPC "wiff-pick", with WFPC2, which a camera that had optical correction built in.

Hellmuth Walter

designed the Starthilfe (takeoff assist) rocket propulsion units for the Messerschmidt Me 163 and the vertical-takeoff Bachem Ba 349 aircrafts, used by the German Luftwaffe in World War II. He also was awarded a patent in 1925 for suggesting that a catalyzed decomposition of hydrogen peroxide could provide oxygen for combustion.

Pistil

female reproductive organ of the flower, is composed of leaf-like carpels. The ovary-containing ovules are at the base of the pistil, while a tube called a style topped by a sticky, pollen-receptive stigma rises from the ovary. There may be one or many pistils in each flower.

Gauge bosons (sometimes called vector bosons)

fundamental [blank] that carry the forces of nature. That is, forces result from particles emitting and absorbing [blank]. The strong nuclear force is carried by gluons, the weak nuclear force is carried by the W, Z-, and Z+ particles, the electromagnetic force is carried by the photon, and gravity is carried by the (as yet unobserved) graviton. The name comes from the role of "gauge theories" in describing the forces (which are beyond the scope of this article).

Complex number

i = square root of -1

Hermann Oberth

imagined at the age of 14 a recoil rocket, which could propel itself by exhausting gas from its base. He also lends his name to the Oberth effect, a phenomenon by which rockets operate more efficiently when moving at higher speeds, and formulated the idea behind multiple-stage rocketry. Oberth also mentored many German rocket engineers through the Verein für Raumschiffahrt (Spaceflight Society), whose formation was inspired partially by Oberth's writing.

Homer Hickam

inspired by seeing Sputnik fly overhead to study rocketry in his early teens. From his coal-company town in West Virginia, he and his rocket club, The Big Creek Missile Agency, designed modest-sized rockets and won the propulsion category of the 1960 National Science Fair. After serving in Vietnam, Hickam worked at the US Army Missile Command in Germany and Huntsville. Later, he moved to NASA, where he specialized in astronaut training. He trained crews for the Hubble Space Telescope's deployment extra-vehicular activity (EVA) and the first two servicing missions.

Konstantin Tsiolkovsky

interest in science manifested first through his science fiction writings, but he gained more notoriety for his eponymous rocket equation. The Tsiolkovsky equation, as published in 1903's Exploration of Outer Space by Means of Rocket Device, relates a rocket's speed with its mass, the speed of its exhaust, and the exhaust's mass (an application of Newton's laws of motion.) The equation is also connected with the idea of specific impulse, a measure of a rocket's efficiency. Tsiolkovsky also published theoretical studies on the capabilities of multi-stage, liquid-fueled engines, gyroscopes, and escape velocities.

A Fourier fur-ee-ay series

is a way to rewrite (almost) any periodic function in terms of only sine and cosine functions.

function

is an association between input values and output values, in which each input value is associated with exactly one output value. That association is often given by a formula, and it is that sort of function that this article will focus on. However, a function could be defined in other ways, such as by a table (as one might make for scientific observations) or simply by a description (for instance, your distance from home is a function of the time of day, since at each time of day you are at exactly one place, and therefore a particular distance from home).

Mercury (Hg, 80)

is one of just two elements that is a liquid at standard temperature and pressure (the only other one is bromine). It has been known since antiquity, and is found in ores such as cinnabar. Older names for it, reflecting its liquid nature, include hydrargyrum (the source of its symbol) and quicksilver. Because it is a very dense liquid, it is commonly used in barometers to measure atmospheric pressure; the pressure exerted by the atmosphere equals the pressure exerted by a column containing 760 millimeters of mercury. Alloys of ______________ with other metals are called amalgams, some of which have been used as dental fillings. Chronic exposure to mercury can cause psychological problems; its use in hatmaking led to the expression "mad as a hatter." More recently, concerns about _______________ exposure have led to the banning of ______________ in thermometers.

"range"

is sometimes used instead of "codomain," but "range" is also sometimes used to mean "image" (see below), so "range" is confusing and NAQT generally avoids it.

Hydrogen (atomic symbol H, atomic number 1)

is the first element on the periodic table and, by far, the most common element in the Universe. In addition to the main isotope (also called protium), there are two other significant isotopes of ______________-: deuterium (2H or D), which has one neutron, and tritium (3H or T), which has two neutrons. It naturally exists as a diatomic gas (H2), which was discovered by the British chemist Henry Cavendish. _____________ is highly flammable when exposed to high temperatures or electric current, a fact demonstrated by the Hindenburg disaster. It can react with nonmetals by losing an electron to form the H+ ion, or react with metals to form the hydride ion, H-.

Helium (He, 2)

is the lightest noble gas and the second most abundant element in the Universe (after hydrogen). Discovered by Sir William Ramsey, Pierre Janssen, and Norman Lockyer, it has two stable isotopes, __________-3 and ____________-4, with ___________-4 by far the more common. Because of their different quantum properties (the ________-3 nucleus is a fermion, while the __________-4 nucleus is a boson), the isotopes of ________ actually have significantly different physical properties. ________-4 can exist in a zero-viscosity state known as superfluidity when its temperature drops below the lambda point. ______ has the lowest boiling point of any element; liquid _________ is used for devices that need intense cooling, such as MRI machines. Most _________- on Earth results from radioactive decay, since the ________ nucleus is equivalent to an alpha particle.

Nitrogen (N, 7)

is the most abundant element in Earth's atmosphere. ___________, which was first isolated as "noxious air" by Daniel Rutherford, exists primarily as a diatomic molecule containing two triple-bonded _______________ atoms (N2). Because _________________ gas is extremely stable, N2 is unusable for many biological and chemical purposes. To make it useful, it often undergoes fixation to convert it into usable _____________ species such as the ammonium ion (NH4+) — as it is by bacteria in the root nodules of legume plants—or ammonia gas (NH3), as is done industrially in the Haber-Bosch process. Conversely, its stability makes it useful in preventing unwanted combustion reactions. It also has a relatively low boiling point (-196°C), which makes liquid _____________ useful as a refrigerant.

Aluminum (Al, 13)

is the most common metal in Earth's crust, and the first metal in the p block of elements. First isolated by Hans Christian Ørsted, its primary ore is bauxite, from which it is refined using large amounts of electric current, via electrolysis, through the Bayer and Hall-Héroult processes. (Because ____________- exists only in a +3 oxidation state, it takes three moles of electrons to produce one mole of _________-; as a result, it has been estimated that 5% of all electricity in the U.S. goes to purifying ___________.) It is found in the mineral corundum, which is found in many gems, including sapphires and rubies; the specific impurities found in a gem determine its color. It is also found in aluminosilicates, such as feldspar.

Iron (Fe, 26)

is the most common metal in the Earth, and one of the major components of the Earth's core. __________ was known to the ancients; its atomic symbol comes from the Latin name ferrum. ________- is the namesake of ferromagnetism; one of its ores is magnetite, Fe3O4, which contains __________ in both of its most common oxidation states, 2+ and 3+. Iron(II) sulfide, FeS2, is formally known as pyrite, but because of its appearance has long been known as fool's gold. _________ can react with oxygen in the air to form __________(III) oxide, Fe2O3, in a relatively slow but exothermic process; this process is used in "all-day" heat patches. Hydrated ________(III) oxide is better known as rust; rust only forms when _________ is exposed to both oxygen and water. Its isotope 56 is "doubly magic" in that its nucleus has 28 protons and 28 neutrons; 28 is a "magic number" that carries special stability. As a result, ____________-56 is one of the most stable of all nuclei, and it is the heaviest nucleus that is normally produced during stellar nucleosynthesis. The largest use of ________ is in steel.

The fundamental theorem of algebra

is the statement that every single-variable polynomial, other than constants, has a root in the complex numbers, which means that if f(x) is a polynomial, then the equation f(x) = 0 has at least one solution where x is some complex number.

The Abel-Ruffini theorem, also called Abel's impossibility theorem,

is the statement that there is no way to find a formula for the solutions of all quintic or higher-degree polynomials, if the formula must be based on the traditional operations (addition/subtraction, multiplication/division, and exponentiation/taking roots).

Oxygen (O, 8)

is, by mass, the most common element in Earth's crust. It was discovered independently by Carl Scheele and Joseph Priestley; Priestley originally called it "dephlogisticated air." _____________-- normally exists in elemental form as a diatomic gas (O2), but it can also exist in a triatomic form, ozone (O3), which is known for its role in blocking UV rays in Earth's stratosphere. Diatomic _____________ is — despite having an even number of electrons — paramagnetic, meaning it has unpaired electrons. This points out a problem with traditional valence bond theories, which predict that ___________ should be diamagnetic; molecular orbital theory correctly explains this behavior. Because __________ is easily capable of accepting electrons, reactions in which a species gives up electrons are known as oxidation reactions.

Sergei Korolev

known until his death by the pseudonym "Chief Designer", headed design and construction for the Soviet long-range ballistic missile program, as well as the R-7 ICBM program. This work urged similar innovations in the U.S. Earlier in his career, Korolev designed a rocket-powered glider, though he was imprisoned and forced into slave labor during the Great Purge. In the 1950s, he personally oversaw Sputnik and Sputnik 2, and he returned to the R-7, modifying it for lunar insertion of robotic probes. His final years were spent devising soft-landing methods for manned lunar missions.

The Apollo-Soyuz Test Project

marked a definite end to the Space Race, and was a symbol of the de-escalation of tensions between the US and the USSR. Deke Slayton, an original Mercury 7 astronaut grounded for medical reasons until 1973, was accompanied by Tom Stafford and Vance Brand on the last launch of Apollo before the advent of the Space Shuttle. The mission demonstrated that two dissimilar spacecraft could rendezvous and dock while in space (an Apollo Command Module and Soyuz 19 docked), and also enabled the crew of Soyuz to photograph the Sun's corona through an artificial eclipse created by the Apollo spacecraft. Each spacecraft also carried out independent experiments.

Leptons

one of the classes of "fundamental particles" (meaning that they cannot be broken down into smaller particles). There are six "flavors" of [blank]: the electron, the muon, the tauon, the electron neutrino (usually just called "the neutrino"), the muon neutrino, and the tauon neutrino. The three neutrinos are neutral and nearly massless (they were once thought to be entirely massless), while the other three have a charge of -1. All neutrinos are fermions, and the total number of [blank] is always conserved (counting regular [blank] as +1 particle and anti-[blank] as -1 particle). The word "[blank]" comes from the Greek for "light" (the opposite of "heavy," not illumination), even though the muon and tauon are relatively massive.

Fermions

particles with half-integral spin. Spin is a form of "intrinsic angular momentum," possessed by particles as if they were spinning around their axis (but they aren't). The values cited for spin are not (usually) the real magnitude of that angular momentum, but the component of the angular momentum along one axis. Quantum mechanics restricts that component to being n/2 times Planck's constant divided by 2π for some integer n. If n is even, this results in "integral" spin, if it is odd, it results in "half-integral" spin. Note that the exact value of the spin itself is a real number; it's the multiplier of h/2π that determines whether it is "integral" or not. The most significant thing about [blank] is that they are subject to the Pauli Exclusion Principle: No two [blank] can have the same quantum numbers (i.e., same state). The name "[blank]" comes from the name of the Italian-American physicist Enrico [blank].

Bosons

particles with integral spin. All particles are either [blank] or fermions. The spin of a composite particle is determined by the total spin (i.e., the component of its intrinsic angular momentum along one axis) of its particles. For instance, an alpha particle (two protons and two neutrons) has four half-integral spin values. No matter how they are added up, the result will be an integral spin value (try it!), so an alpha particle is a (composite) [blank]. The Pauli Exclusion Principle does not apply to [blank] (in fact, [blank] prefer to be in the same quantum state). The name "[blank]" comes from the name of the Indian-American physicist Satyendra Nath Bose.

The Davisson-Germer experiment (1923-1927)

performed by Clinton Davisson and Lester Germer, confirmed the de Broglie hypothesis by showing that electrons can exhibit wave-like behavior. The experimenters fired electrons at a nickel crystal, and measured the diffraction patterns using an electron counter called a Faraday box (or Faraday cup) mounted on an arc so that it could detect electrons emitted at various angles. The peak intensity was observed at 50 degrees and 54 electronvolts, corresponding to the diffraction predicted for X-rays by Bragg's law. (Note that diffraction is a property of waves, not particles, and thus could only be observed if electrons can act as waves.)

The Millikan oil-drop experiment (1909)

performed by Robert A. Millikan and Harvey Fletcher to measure the charge of the electron. In the first step, the terminal velocity of an oil drop was measured, which means that the drag force (which can be calculated using Stokes' law) equals the force of gravity. From this, the mass can be calculated. Then, by turning on an electric field, the particle starts to move upward with a terminal velocity when the electric force balances out the forces of gravity and drag. Using this, and the mass of the drop, the total charge on the drop can be calculated. Millikan and Fletcher found that the total charge on the drops were always quantized—that is, always an integer multiple of some constant; specifically, the constant they found is about 1.59 × 10-19 coulombs, within 1% of the currently accepted value.

Gregor Mendel's experiments with pea plants (1860s)

pioneered the studio of genetics. Mendel, an Austrian monk, proposed the law of segregation, which holds that each organism has two alleles for each trait, which are segregated into gametes so that each gamete inherits one copy, as well as the law of independent assortment, which says that genes for individual traits are inherited independently. He supported both of those laws with experimental evidence by growing and counting pea plants. He worked with seven characteristics including plant height, seed shape, and color. His experiments primarily consisted of hybridizing plants with certain characteristics, and observing what fraction of the next generation had certain traits. His results were remarkably close to the values that would be predicted from modern genetics—close enough, in fact, that Mendel has been accused of manipulating his data.

unit circle

points and segments related to a circle of radius 1 centered at the origin

The Meselson-Stahl experiment (1958)

proved that DNA replication is semiconservative, meaning that when a double-helix strand of DNA is duplicated, the result is two double-helix strands, each of which has one helix from the parent molecule and one newly-synthesized helix. Matthew Meselson and Franklin Stahl used E. coli grown in a medium containing only nitrogen-15; they were then allowed to synthesize DNA in an environment containing only nitrogen-14 over two generations. The net result was that in the second generation, half the DNA molecules contained nitrogen-15 in one strand and nitrogen-14 in the other, while the other half of the molecules contained only nitrogen-14.

SM3A

replaced failed gyroscope systems.

SM3B

replaced the Faint Object Camera (FOC) with the Advanced Camera for Surveys (ACS), and also repaired NICMOS, which was installed during SM2.

SM2

replaced the Goddard High-Resolution Spectrograph (GHRS) and Faint Object Spectrograph (FOS) with improved successors.

Odd functions

satisfy the rule f(-x) = -f(x) for every x in the domain of the function. The graph of an odd function remains the same when it is rotated 180° around the origin. Odd functions are so named because if a polynomial's exponents (on the variable) are all odd, then the polynomial is an odd function; for instance, x3, 4x7, and -x5 + 2x3 are all odd. There are other odd functions, such as the sine and cube root functions.

Even functions

satisfy the rule f(-x) = f(x) for every x in the domain of the function. The graph of an even function has reflection symmetry over the y-axis. Even functions are so named because if a polynomial's exponents (on the variable) are all even, then the polynomial is an even function; for instance, x2, 3x6, and -x8 + 7x4 are all even. There are other even functions, though, such as the cosine and absolute value functions.

Apollo 11

saw the first Moon landing and moonwalk by astronauts Neil Armstrong and Buzz Aldrin (astronaut Michael Collins piloted the Command Module in lunar orbit and never walked on the moon). After the Lunar Module landed in the Sea of Tranquility, Armstrong said, "Houston, Tranquility Base here. The Eagle has landed." Later stepping onto the lunar surface, he said, "That's one small step for [a] man, one giant leap for mankind." According to Chris Kraft, NASA officials chose Armstrong as the first to walk on the Moon because he was more humble than Aldrin, and because he was the Commander. However, the stated reason was that Armstrong's seat was closer to the door. ______________, like other Apollo missions, launched atop a Saturn V booster.

Trigonometric functions

sine, cosine, tangent, cosecant, secant, and cotangent functions. There are many interesting relationships between these: the graphs of sine and cosine are translations of each other; the tangent function equals the sine function divided by the cosine function; the cosecant, secant, and cotangent functions are the reciprocals of the sine, cosine, and tangent functions, respectively; and there are many other relationships called trigonometric identities.

The Rutherford gold foil experiment (1908-1913)

sometimes named after Rutherford's assistants Hans Geiger and Ernest Marsden, discovered the positively-charged nucleus of the atom; as a result, it disproved J. J. Thomson's plum pudding model. The experimenters fired alpha particles (helium nuclei) at a sheet of gold foil. (They also used other elements, including silver.) The scattered particles were detected by a screen containing zinc sulfide, which fluoresced when the alpha particles hit it. While most of the alpha particles went straight through the foil with minimal scattering, a small fraction of alpha particles were reflected back at the source. This result was unexpected, as backscattering could only occur if the alpha particles were colliding with a particle massive enough to reverse their momentum. Rutherford said "It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

Petals

specialized leaves, often brightly colored to attract pollinating species. Collectively, they are called a corolla.

Continuous functions

studied in calculus, are functions where the limit approaching each point equals the function's value at that point. In particular, there are no holes, jumps, or asymptotes "in the middle of the graph."often explained as a function's graph being drawable in one motion without lifting the writing utensil from the paper. All polynomials are ________________, as are the sine and cosine functions, exponential and logarithmic functions, and the absolute value function. Some examples of non-_______________- functions are many rational functions, as they often have holes or asymptotes; the tangent, cosecant, secant, and cotangent functions, which have asymptotes; and the floor and ceiling functions, which have jumps.

The launch of Sputnik 1

the first artificial satellite, by the USSR kicked off the so-called "Space Race." The Space Race was manifestation of the Cold War where successes in launching objects and people into space was seen as a proxy for capacity to build intercontinental ballistic missiles. ____________________ was originally intended to carry many scientific instruments, but those instruments were descoped, in favor of a simple radio transmitter. That transmitter broadcasted a "beep" at a specified interval, allowing scientists to map its deceleration as a result of atmospheric drag. _______________ was followed by Sputnik 2, which carried a dog named Laika (meaning "barker") into low-earth orbit, and was destroyed upon re-entry.

Gluons

the gauge bosons that carry the strong nuclear force and bind hadrons together. [blank] have no charge and no mass, but do have color (in the sense of quarks). This color cannot be observed directly because the [blank] are part of the larger hadron. The name comes from their role in "gluing" quarks together.

Io

the innermost of the four Galilean moons of Jupiter (the moons discovered by Galileo), the fourth-largest moon in the solar system, the densest moon, and the most geologically active body in the solar system, with more than 400 volcanoes. Io's features are named for characters from the Io story in Greek mythology; fire, volcano, and thunder deities from other mythologies; and characters from Dante's Inferno. Io plays a significant role in shaping Jupiter's magnetosphere. Pioneer 10 first passed by Io in December 1973.

Ganymede

the largest moon in the solar system and the only one known to have its own magnetosphere. The third of the Galilean satellites, Ganymede was also first photographed close-up by Pioneer 10 in 1973. Galileo made six flybys of Ganymede between 1996 and 2000. Based on a suggestion from Simon Marius, Ganymede (along with many of the Jovian satellites) is named for one of Jupiter's lovers in Roman mythology; Ganymede is the only such moon named for a male figure. Many of Ganymede's features, including the Enki Catena, are given names from Egyptian and Babylonian mythology, although its largest dark plain is Galileo Regio. Ganymede is scheduled to be orbited by the European Space Agency's Jupiter Icy Moon Explorer (JUICE), currently slated for a 2022 launch.

Titan

the largest moon of Saturn and the second largest in the solar system. Until Voyager 1 visited in 1980, it was thought to be larger than Ganymede. It is the only known satellite with a dense atmosphere — so dense that it makes observation of surface features nearly impossible except from close up — and also the only known satellite for which there is evidence of stable bodies of surface liquid. Discovered in 1655 by Christiaan Huygens, it was visited by the Cassini-Huygens mission in 2004. Titan's albedo features, such as the highly reflective area Xanadu, are named for sacred or enchanted places from world literature and mythology. Because of its nitrogen-rich atmosphere and the presence of surface liquid, Titan is often thought to be the most likely place in the solar system for microbial life to exist outside of Earth.

domain

the set of possible input values for a function

codomain

the set of possible output values is called the .

Vostok 1 and Vostok 6

transported the first human and the first woman into space (respectively, Yuri Gagarin and Valentina Tereshkova). Gagarin's April 12, 1961 flight is still celebrated as Yuri's Night. During ______________________, Gagarin completed a single orbit around Earth before re-entering and parachuting out of his capsule. ____________________- was largely uneventful, though Tereshkova did note minor physical pains and also could not reach the scientific experiments aboard. Both ______________ used Vostok-K boosters.

The Miller-Urey experiment (1952)

was an attempt to demonstrate a possible mechanism—proposed by John Haldane and Alexander Oparin—for how life could form from inorganic chemicals. Stanley Miller and Harold Urey modeled Earth's prebiotic atmosphere as a mixture of water, methane (CH4), ammonia (NH3), and hydrogen. They allowed those four substances to react in an apparatus over a one-week period; the apparatus included a heater to convert the water to water vapor and an electrode to simulate lightning strikes. The resulting mixture contained more than 20 distinct amino acids that formed spontaneously; a more modern "volcanic" version of the experiment produced even more amino acids by including sulfur compounds.

Apollo 1

was intended to be a test of the Command/Service Module in low-Earth orbit (LEO). However, a fire on the launchpad during a test killed the three astronauts aboard (Virgil "Gus" Grissom, Roger Chaffee, and Ed White). The fire was exacerbated by the pure-oxygen, positive-pressure environment inside the capsule, and the fact that the capsule door opened inward. Both of these design elements were scrapped in subsequent missions, and the second was replaced with an outward-opening hatch nominally to facilitate spacewalks. Lessons learned from _________________ were also taken into account during the design of the Space Shuttle.

Gold (Au, 79)

was known to the ancients as a relatively inert metal. Its atomic symbol comes from its Latin name, aurum. It is resistant to attack by most acids, but it (along with platinum) will dissolve in aqua regia, a mixture of concentrated nitric acid and hydrochloric acid. Among all metals, it has the highest electronegativity and electron affinity; it occasionally is found in a -1 oxidation state as Au-. Widely used in jewelry, it also has a number of scientific uses. Ernest Rutherford's ______ foil experiment demonstrated the existence of a positively charged nucleus. Scanning electron microscopy (SEM) often requires that specimens be "sputtered," or thinly coated, with____________atoms to allow imaging. Suspensions of ________compounds have been used to treat rheumatoid arthritis.

Apollo 13

was supposed to land in the Fra Mauro region of the Moon. An improperly-refurbished No. 2 oxygen tank and subsequent improper repairs caused the tank to rupture during a routine "cryo-stir" before entering lunar orbit. The explosion also damaged the No. 1 oxygen tank and caused further leakage. To bring back the astronauts, the orbiter was put on a free-return trajectory around the Moon. NASA engineers also solved power-management, water-conservation, and trajectory planning problems with the help of Ken Mattingly, the primary Command Module pilot who had been grounded due to exposure to German measles. All three astronauts returned to Earth safely, and the landing site was re-assigned to the subsequent Apollo 14 mission.

SpaceX CRS-1 (also called SpX-1 or CRS-1)

was the first commercial mission to resupply the International Space Station (ISS). A structural failure in one of the nine Merlin engines that make up the Falcon 9 rocket first stage necessitated a longer burn with the remaining eight engines. That correction resulted in a proper orbital insertion for the primary payload (a Dragon resupply vehicle), but an unstable, decaying orbit for its secondary payload (an ORBCOMM satellite). This was taken as a proof of concept by SpaceX for the redundant, multiple-engine design. The craft successfully berthed with the ISS and successfully carried out its primary mission, re-supplying the space station and returning cargo to Earth.

Sulfur (S, 16)

was widely known in the ancient world, and is referred to in the Bible as brimstone. Its nature as an element was first recognized by Antoine Lavoisier. Its most stable allotrope is an eight-membered ring that exists as a yellow solid. It is most often isolated by injecting superheated steam into the ground in the Frasch process. As an element, it is used in the vulcanization process to cross-link the polymer strands of rubber to increase strength; similarly, sulfur-sulfur bonds hold many proteins together. Industrially, though, the majority of ___________ is used to make sulfuric acid, H2SO4 (in fact, sulfuric acid is the most widely produced chemical in the chemical industry). ___________ compounds are noted for their strong and unpleasant odors; small quantities of hydrogen sulfide, H2S, are frequently added to natural gas — which is normally odorless — to help people notice gas leaks.

Voskhod 1 and Voskhod 2

were the only two missions of the __________ program, and were superseded quickly by the Soyuz program. The spacecrafts made use of Sergei Korolev's designs. Korolev himself was preoccupied with the Moon race, again in a position of favor after the fall of Khrushchev (though Korolev died before the designs were used). _____________ was the first flight to contain multiple astronauts, and _______________ was the platform for the first EVA (extra-vehicular activity or "spacewalk"). Alexey Leonov, who conducted the spacewalk on ____________________, also participated in the later Apollo-Soyuz Test Project.

asymptotes

which are places in which their graphs approach a line (or occasionally other shape), usually getting infinitely close to but not crossing it.

Thomas Young's double-slit experiment (circa 1800)

which predated the development of quantum mechanics by over a century, demonstrated that light can behave as either a wave or a particle. After passing a beam of light through two narrowly spaced slits, Young observed the characteristic light and dark fringes of interference seen when light acts as a wave. More modern versions that add detectors showing which slit the light passes through, however, show that the light passes through one slit or the other, acting as photons; moreover, the interference pattern disappears. A modern variant, called a quantum eraser, demonstrates quantum entanglement (the ability to exchange information over large distances instantaneously).