Perspectives Midterm

Euler

Invented graph Theory Proved e to be irrational

Descarte's great mathematical invention linked geometry and numbers, suddenly turning geometry by the use of graphs into what type of math?

Analytic Geometry

Who disproved phlogiston?

Antoine Lavoisier; hated during scientific revolution because he was a tax collector (aristocrat)

Janos Bolyai and Nikolas Lobochevsky both worked independently on?

Hyperbolic Geometry or non-Euclid geometry; early 19th century; what happens when we are not in a flat surface.

What is ether in Aristotle's mind?

Invisible matter around the Earth; have to have material hold you up; was wrong but not found out till much later.

Who was Leonardo of Pisa and what was his most famous contribution?

Italian mathematician who created the Fibonacci numbers

What nationality was Euclid?

Greek

Who are the Cartesian Coordinates named after?

Descartes

Which kind of numbers, Pythagoras, 6th B.C., who lived on a Greek island near Turkey, called Samos, abhorred?

Irrational numbers; legend says that one of his followers was pushed into water and drowned because he wanted to announce to the world that irrational numbers were a real thing.

The two inventors of calculus are?

Isaac Newton and Gottfried Leibniz

Who wrote in 1687 "Mathematical Principles of Natural Philosophy"?

Isaac Newton; enlightenment period that studied science

What was Copernicus' book, the revolutions, about?

It discussed and gave a detailed explanation of the heliocentric theory of the universe. Described astronomy and revolutions of the planets. Helped sove the calendar problem (his calculations helped determine the new Gregorian calendar)

Who developed the prime mover theory with a system of 56 celestial spheres?

Aristotle's astronomical system (two domains, the astronomical-heavenly and the sublunary-Earth) was linked together by a series of interconnection spheres, 56 total. The outermost sphere was called the prime mover, because all the other spheres were linked to it and derived their motion from it. However, Aristotle never explained what moved this prime mover to get the whole system started. So the church used this as a way to prove that God existed.

Why is Mendeleev recongized as the creator of the periodic table?

Because he was able to leave blank spaces and predict the density and weight of these atoms; did not leave room for noble gases

Carl Gauss

Bell curve Built theory of complex numbers into its modern form First to prove rigorously the Fundamental Theorem of Algebra Prince of Mathematics

George Boole

Boolean algebra and analysis "Discoverer of pure mathematics"

Who was the first person to use negative numbers and zero in arithmetic?

Brahamupta; negative numbers first seen as debts

The Prince of Mathematics is?

Carl Friedrich Gauss; discovered the arithmetic sequence; Guassian curves named after him

Who wrote "Megiste" (The greatest) and what is it about?

Claudius Ptolemy; it was about geocentric system; his geocentric system was based on Aristotle's but simplified and modernized; idea of prime mover was close to existence of God; Ptolemy was not related to the Ptolemy family of rulers

What is phlogiston?

Combustible (Flammable) material; thought to be in every piece of material flammable

Georg Cantor

Created modern set theory Gave modern definition of irrational numbers

Which mathematician during the 1900 Mathematics conference in Paris provided a list of 23 major problems yet to be solved?

David Hilbert

Which mathematician did not flee from Nazi Germany

David Hilbert, one of the most famous mathematicians

Who provided a list of 23 Unsolved problems?

David Hilbert; directed the development of the 20th-century mathematics

In honor of who did Dalton name indivisible matter atoms?

Democritus

Jacob and Johann Bernoulli

Developed exponential calculus, important methods for integral and differential equations Coined the world integral Family rivalry

What was alchemy about?

Discovered phosphorus, fermentation, distillation, crystallization, also rely on magic and dreams so non-scientific evidence in their work

Henri Poincare

Effectively discovered chaos theory Made major advances in theory of differential equations Helped world recognize the importance of new physical theories of Einstein and Planck

Which ancient civilization used the base-ten (decimal) system, had no concept of place value and did not solve mathematical problems using proofs?

Egyptians; Elaborate proofs not their thing; had to use different hieroglyphics because they didn't have place value.

Pi, e, and i are all symbols popularized by?

Euler who became blind at the end of his life and was still able to do elaborate proofs, in his head, and told them to someone else who wrote them for him

Nicolai Lobachesky

Famous for discovering non-Euclidean geometry Maybe first to distinct difference between continuous and differentiable curves "There is no branch of mathematics...which may not someday be applied to the phenomena of the real world."

Rene Descartes

Father of Modern Mathematics Inventor of analytic geometry and symbolic algebraic notation

Who is famous for inventing modern number theory and his last theorem which took centuries to be proven?

Fermat; Fermat's last theorem (no three positive integers a, b, and c satisfy the equations a^n + b^n = c^n for any value of n greater than n).

Leonardo Pisano

Fibonacci numbers Introduced decimal system and other new methods of arithmetic to Europe Famous for his book "Liber Abaci"

Pythagoras

First pure mathematician Believed all things were numbers and related music to math Pythagorean Theorem

Hypatia

First woman to make a substantial contribution to the development of mathematics Head of the Platonist school at Alexandria Commentator on the "Conics of Apollonius and Arithmetica" by Diophantus Murdered by a Christian mob

What about Bohr?

Fixed energy and orbits, otherwise would fall into positive nucleus; energy that it admitted while performing this jump was released as a radiation that was emitted in the form of light

Pierre Fermat

Founded Number Theory Little Theorem Last Theorem Developed system of analytic geometry Developed methods of differential and integral calculus

Thales

Founded the Milesian School of natural philosophy Developed scientific method Believed that everything came from water Founded the geometry of lines Given credit for introducing abstract geometry Reportedly used his skills at recognizing weather patterns

Euclid

Founded the school of mathematics at the University of Alexandria First to prove that there are infinitely many prime numbers Wrote the Elements

From the Antiquity to the Middle Ages, knowledge was passed down from _______ to _______?

Greeks to Arabics to Western World

What is J.J. Thomson contribution to the atomic model?

He described the structure like raisin pudding. He said the electrons were the raisins embedded and were balanced out by a positive electric in the pudding part of the atom

What was the name of a great center of knowledge created in Baghdad in order to revive the spirit of the great library of Alexandria?

House of Wisdom

What was Thomas Young's double slit experiment about?

Light experiment; light traveled in a wave like pattern; tested by passing light through one slit that projected onto another screen with two slits, and then onto a dark film that shows the interference pattern of the different light waves; hypothesis tested true

Bernard Riemann

Modern physics relies on Riemann's notion of geometry of space Master of complex analysis "every line through a point not a given line meets that given line."

Brahmagupta

One of the first to express equations with symbols rather than words Solved general quadratic equation

Who is the famous Greek philosopher founded the Academy in Athens and used the dialectic as a teaching method?

Plato

Archimedes

Principles of leverage First law of hydrostatics Killed by a Roman Soldier Proved that the volume of a sphere is 2/3 the volume of a circumscribing cylinder

Way to remember the order of Greek philosophers?

SPA: Socrates Plato Aristotle

Where does the sixty-based system come from?

Sumerians/Babylonians in Mesopotamia

What is called Euclid's famous 13-volume encyclopedia?

The Elements; what we teach in middle and high shool

What are Galileo's most famous books, concerning Astronomy?

The Starry Messenger Dialogue on the Two Chief World Systems: Is about a conversation between a scientist and someone who is uneducated, but in reality it is about Galileo and the Pope, respectively, arguing over which system is correct. The pope was not happy about it.

What are Newton's corpuscules?

The small particles that he proposed light consists of. He said they are shot out form the source of the light. It was in direct contrast to an existing theory that stated that light consists of waves, which was supported by Thomas Young. Turns out they were both right.

Why were the Egyptians interested in mathematics? How did the Egyptians estimate the area of a disc?

They were only interested in purposeful mathematics; didn't do proofs. They used math to determine how much land they were able to tax after the floods.

Who revived Aristotelian theories in the Middle Ages?

Thomas Young who went to school in Couldava, Spain and could speak Latin, English, and Arabic. He pretended to be a Muslim student and translated Arabic works into Latin or English so everyone could read it.

Isaac Newton

Three laws of motion: inertia, force, reciprocal action Father of Calculus Published "Philosophize Naturalis Principe Mathematica"

Whose data did Kepler base his three laws on?

Tycho Brahe who isolated himself and his sister on an island and mapped the sky and collected data for other scientists; tracked the planets throughout their entire orbit without the aid of a telescope; proposed that they orbited in perfect circles with a few epicycles mixed in

What is vitalism about?

Up until 19th century, it was believed organic material couldn't be made without source of life. Friedrich Wohler in 1848 proved this wrong.

Who invented Algebra?

al-Khwarizmi; algebra was named after him. Diophantus was the other one.

Gottfried Leibniz

co-inventor of infinitesimal calculus Built first calculator that could do multiplication Mathematical innovations include differential and integral notations, concepts of matrix determinant, Gaussian elimination, and binary number system