Fibonacci
Numerical coincidences in numbers from the physical world 1. Length of six weeks 2. Speed of light 3. Earth's diameter 4. Gravitational Acceleration
1. The number of seconds in six weeks, or 42 days, is exactly 10! (ten factorial) seconds. Many have recognized this coincidence in particular because of the importance of 42 in Douglas Adams' The Hitchhiker's Guide to the Galaxy. 2. The speed of light is (by definition) exactly 299,792,458 m/s, very close to 300,000,000 m/s. This is a pure coincidence, as the meter was originally defined as 1/10,000,000 of the distance between the Earth's pole and equator along the surface at sea level, and the Earth's circumference just happens to be about 2/15 of a light-second.[27] It is also roughly equal to one foot per nanosecond (the actual number is 0.9836 ft/ns). 3. The polar diameter of the Earth is equal to half a billion inches, to within 0.1% 4. While not constant but varying depending on latitude and altitude, the numerical value of the acceleration caused by Earth's gravity on the surface lies between 9.74 and 9.87, which is quite close to 10. This means that as a result of Newton's second law, the weight of a kilogram of mass on Earth's surface corresponds roughly to 10 newtons of force exerted on an object.[29] This is actually related to the aforementioned coincidence that the square of pi is close to 10. One of the early definitions of the meter was the length of a pendulum whose half swing had a period equal to one second. Since the period of the full swing of a pendulum is approximated by the equation below, algebra shows that if this definition was maintained, gravitational acceleration measured in meters per second per second would be exactly equal to the square of pi When it was discovered that the circumference of the earth was very close to 40,000,000 times this value, the meter was redefined to reflect this, as it was a more objective standard (because the gravitational acceleration varies over the surface of the Earth). This had the effect of increasing the length of the meter by less than 1%, which was within the experimental error of the time.[citation needed]
How to draw a kelper triangle (listed steps)
A Kepler triangle can be constructed with only straightedge and compass by first creating a golden rectangle: Construct a simple square Draw a line from the midpoint of one side of the square to an opposite corner Use that line as the radius to draw an arc that defines the height of the rectangle Complete the golden rectangle Use the longer side of the golden rectangle to draw an arc that intersects the opposite side of the rectangle and defines the hypotenuse of the Kepler triangle
scrum poker benefits
A study by Moløkken-Østvold and Haugen[5] found that [the] set of control tasks in the same project, estimated by individual experts, achieved similar estimation accuracy as the planning poker tasks. However, for both planning poker and the control group, measures of the median estimation bias indicated that both groups had unbiased estimates, as the typical estimated task was perfectly on target. In other words, planning poker can be as good as expert estimation - thereby avoiding the Dunning-Kruger effect.
golden angle algebraically
Algebraically, let a+b be the circumference of a circle, divided into a longer arc of length a and a smaller arc of length b The golden angle is then the angle subtended by the smaller arc of length b.
Applications of Fibonacci numbers
Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings,[10] such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple,[11] the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts.[12]
scrum poker procedure
At the estimation meeting, each estimator is given one deck of the cards. All decks have identical sets of cards in them. The meeting proceeds as follows: A Moderator, who will not play, chairs the meeting. The Product Manager provides a short overview of one user story to be estimated. The team is given an opportunity to ask questions and discuss to clarify assumptions and risks. A summary of the discussion is recorded by the Project Manager. Each individual lays a card face down representing their estimate for the story. Units used vary - they can be days duration, ideal days or story points. During discussion, numbers must not be mentioned at all in relation to feature size to avoid anchoring. Everyone calls their cards simultaneously by turning them over. People with high estimates and low estimates are given a soap box to offer their justification for their estimate and then discussion continues. Repeat the estimation process until a consensus is reached. The developer who was likely to own the deliverable has a large portion of the "consensus vote", although the Moderator can negotiate the consensus. To ensure that discussion is structured; the Moderator or the Project Manager may at any point turn over the egg timer and when it runs out all discussion must cease and another round of poker is played. The structure in the conversation is re-introduced by the soap boxes. The cards are numbered as they are to account for the fact that the longer an estimate is, the more uncertainty it contains. Thus, if a developer wants to play a 6 he is forced to reconsider and either work through that some of the perceived uncertainty does not exist and play a 5, or accept a conservative estimate accounting for the uncertainty and play an 8.
Fibonacci economics
Brock-Mirman economic growth model.
Kepler
December 27, 1571 - November 15, 1630) was a German mathematician, astronomer, and astrologer. A key figure in the 17th-century scientific revolution, he is best known for his laws of planetary motion, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation.
the journal for Fibonacci numbers
Fibonacci quarterly
gamification
Gamification is the application of game-design elements and game principles in non-game contexts.
johannes kepler on the golden ratio
Geometry has two great treasures: one is the theorem of Pythagoras, the other the division of a line into mean and extreme ratio. The first we may compare to a mass of gold, the second we may call a precious jewel
Tombstone epitaph for Kepler
I measured the skies, now the shadows I measure Skybound was the mind, earthbound the body rests
angle subtended meaning
In geometry, an angle subtended by an arc, line segment, or other curve is one whose two rays pass through the endpoints of the arc. The precise meaning varies with the context. For example, one may speak of the angle subtended by an arc of a circumference when the angle's vertex is the centre of the circle to which the circumference belongs. A simple theorem of plane geometry states that arcs of equal lengths subtend equal angles in such a situation.
golden angle
In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the larger arc to the length of the smaller arc is the same as the ratio of the full circumference to the length of the larger arc.
fibonacci sequence
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...
golden ratio and show line segments
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
Dunning-Kruger effect
In the field of psychology, the Dunning-Kruger effect is a cognitive bias wherein persons of low ability suffer from illusory superiority, mistakenly assessing their cognitive ability as greater than it is. The cognitive bias of illusory superiority derives from the metacognitive inability of low-ability persons to recognize their own ineptitude. Without the self-awareness of metacognition, low-ability people cannot objectively evaluate their actual competence or incompetence.[1] As described by David Dunning and Justin Kruger, the cognitive bias of illusory superiority results from an internal illusion in people of low ability and from an external misperception in people of high ability; that is, "the miscalibration of the incompetent stems from an error about the self, whereas the miscalibration of the highly competent stems from an error about others."[1] Hence, the corollary to the Dunning-Kruger effect indicates that persons of high ability tend to underestimate their relative competence, and erroneously presume that tasks that are easy for them to perform also are easy for other people to perform
Introspection
Introspection is the examination of one's own conscious thoughts and feelings.
Kepler rejection
Kepler's laws were not immediately accepted. Several major figures such as Galileo and René Descartes completely ignored Kepler's Astronomia nova.
Fibonaccis book name and when?
Liber Abaci in 1202
metacognition
Metacognition is "cognition about cognition", "thinking about thinking", "knowing about knowing", becoming "aware of one's awareness" and higher-order thinking skills. The term comes from the root word meta, meaning "beyond".[1] Metacognition can take many forms; it includes knowledge about when and how to use particular strategies for learning or for problem-solving.
metamemory
Metamemory or Socratic awareness, a type of metacognition, is both the introspective knowledge of one's own memory capabilities (and strategies that can aid memory) and the processes involved in memory self-monitoring.[1] This self-awareness of memory has important implications for how people learn and use memories. When studying, for example, students make judgements of whether they have successfully learned the assigned material and use these decisions, known as "judgments of learning", to allocate study time.
Rabbits
Outside India, the Fibonacci sequence first appears in the book Liber Abaci (1202) by Fibonacci.[6] Fibonacci considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that: a newly born pair of rabbits, one male, one female, are put in a field; rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was: how many pairs will there be in one year?
scrum poker equipment
Planning poker is based on a list of features to be delivered, several copies of a deck of cards and optionally, an egg timer that can be used to limit time spent in discussion of each item. The feature list, often a list of user stories, describes some software that needs to be developed. The cards in the deck have numbers on them. A typical deck has cards showing the Fibonacci sequence including a zero: 0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89; other decks use similar progressions. The reason for using the Fibonacci sequence is to reflect the inherent uncertainty in estimating larger items.[citation needed] Several commercially available decks use the sequence: 0, ½, 1, 2, 3, 5, 8, 13, 20, 40, 100, and optionally a ? (unsure), an infinity symbol (this task cannot be completed) and a coffee cup (I need a break). Some organizations[which?] use standard playing cards of Ace, 2, 3, 5, 8 and king. Where king means: "this item is too big or too complicated to estimate". "Throwing a king" ends discussion of the item for the current sprint. Smartphones allow developers to use mobile apps instead of physical card decks. When teams are not in the same geographical locations, collaborative software can be used as replacement for physical cards.
Sanskrit prosody
Sanskrit prosody or Chandas refers to one of the six Vedangas, or limbs of Vedic studies.[1] It is the study of poetic metres and verse in Sanskrit.[1] This field of study was central to the composition of the Vedas, the scriptural canons of Hinduism, so central that some later Hindu and Buddhist texts refer to the Vedas as Chandas.
scrum poker
Scrum poker, is a consensus-based, gamified technique for estimating, mostly used to estimate effort or relative size of development goals in software development. In planning poker, members of the group make estimates by playing numbered cards face-down to the table, instead of speaking them aloud. The cards are revealed, and the estimates are then discussed. By hiding the figures in this way, the group can avoid the cognitive bias of anchoring, where the first number spoken aloud sets a precedent for subsequent estimates.
golden ratio and art
Some twentieth-century artists and architects, including Le Corbusier and Dalí, have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.
The Fibonacci numbers are important in
The Fibonacci numbers are important in the computational run-time analysis of Euclid's algorithm to determine the greatest common divisor of two integers: the worst case input for this algorithm is a pair of consecutive Fibonacci numbers
Where does Fibonacci sequence first appear?
The Fibonacci sequence appears in Indian mathematics, in connection with Sanskrit prosody.[8][13] In the Sanskrit tradition of prosody, there was interest in enumerating all patterns of long (L) syllables that are 2 units of duration, and short (S) syllables that are 1 unit of duration. Counting the different patterns of L and S of a given duration results in the Fibonacci numbers: the number of patterns that are m short syllables long is the Fibonacci number Fm + 1.[9]
The Fibonacci sequence is named after
The Fibonacci sequence is named after Italian mathematician Leonardo of Pisa, known as Fibonacci.
the vedas
The Vedas are a large body of knowledge texts originating in the ancient Indian subcontinent. Composed by ancient Aryans in Vedic Sanskrit, the texts constitute the oldest layer of Sanskrit literature and the oldest scriptures of Hinduism.[2][3] Hindus consider the Vedas to be apauruṣeya, which means "not of a man, superhuman"[4] and "impersonal, authorless".[5][6][7]
purpose of scrum poker
The reason to use planning poker is to avoid the influence of the other participants. If a number is spoken, it can sound like a suggestion and influence the other participants' sizing. Planning poker should force people to think independently and propose their numbers simultaneously. This is accomplished by requiring that all participants show their card at the same time.
There are four Vedas:
There are four Vedas: the Rigveda, the Yajurveda, the Samaveda and the Atharvaveda.
two components of meta-cognition
There are generally two components of metacognition: knowledge about cognition, and regulation of cognition
fibonacci sequence as a complete sequence meaning
This means that every positive integer can be written as a sum of Fibonacci numbers, where any one number is used once at most.
apauruṣeya
apauruṣeya, which means "not of a man, superhuman"[4] and "impersonal, authorless"
stochastic
randomly determined; having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely.
Vedas are also called
śruti ("what is heard") literature,[8] distinguishing them from other religious texts, which are called smṛti ("what is remembered"). The Veda, for orthodox Indian theologians, are considered revelations seen by ancient sages after intense meditation, and texts that have been more carefully preserved since ancient times.[9][10] In the Hindu Epic the Mahabharata, the creation of Vedas is credited to Brahma.[11] The Vedic hymns themselves assert that they were skillfully created by Rishis (sages), after inspired creativity, just as a carpenter builds a chariot
