- Created by: Elena
- Created on: 07-07-20 10:23
- Leader of a Greek religious movement that believed all relations could be reduced to number relations "all things numbers"
- Pythagorean theorem was known and used by the Babylonians
- He is credited with the first recorded proof of this theorem
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- Conceived a number of paradoxes as an attempt to support the doctrine that all evidence of the senses is illusory (especially motion)
- One famous example of such a paradox is the race between the famous Greek hero Achilles and a tortoise
- His paradox is resolved with the insight that a sum of infinitely many terms can nevertheless yield a finite result - calculus
- He reasoned that if the tortoise was given a headstart, Achilles would never be able to overtake it, simply reaching points the tortoise had already reached and moved on from
- This provided an early entree into the mathematics of limits
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- Created many inventions, including compound pulley systems, war machines, and even an early planetarium
- His major mathematical writings contributed to understanding the principle of buoyancy, plane equilibriums, and the parabola
- Was the first to give a scientific method for calculating pi, by measuring circumscribed polygons approaching a "limit"
- One of the earliest approaches to "integration"
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- His treatise on mathematics, The Elements, endured for two millennia as a principle text on geometry
- Commences with definitions and 5 postulates
- First three deal with geometrical construction
- Fourth asserts that all right angles are equal
- Fifth states that parallel lines will never meet
- Euclid also proved Pythagoras' theorem independently
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- Viewed all physical bodies as machines operated by mechanical principles (including the human body)
- In analytical geometry, Descartes proposed that a point in a plane could be determined by distances from two fixed lines ('x' and 'y')
- Such coordinates are referred to as "Cartesian coordinates"
- Similarly, a point in 3-dimensional space could be determined by three coordinates (x,y,z)
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- Number theorist who worked on maxima/minima, tangents, and stationary points to become a father of calculus
- Discovered analytic geometry independently of Descartes
- Co-founded probability theory through correspondence with Pascal
- Well-known for his "Enigma", also known as Fermat's Last Theorem
- xn+yn=zn has no solution when n>2
- Investigated a type of Archimedean spiral, named Fermat's spiral
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- Principle contribution was probability theory, the foundations of which were established in a long exchange of letters with Fermat
- Created Pascal's Triangle to calculate odds governing combinations
- Sum of any row gives the total number of combinations
- Pairs of numbers at the end of each row gives the "odds" of the least likely combinations, with each succeeding pair giving chances of combinations which are increasingly likely
- Work in binomial coefficients lead to Newton's later discovery of the general binomial theorem for fractional and negative powers
- Invented the first digital calculator, the "Pascaline"
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- "If I have seen further it is by standing upon the soldiers of giants"
- Principia Mathematica (The Mathematical Principles of Natural Philosophy), contains his "Laws of Motion" and philosophical rules
- His binomial theorem dealt with expanding expressions of (a+b)n
- Regarded as inventing modern calculus with Leibniz, who developed his own version in the same time frame, resulting in a dispute
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- Developed calculus coincident with but independently of Newton, though the integral notation Leibniz developed is more elegant
- Integral sign and derivative notation still in use today
- Attempted to develop an 'alphabet of human thought' in which all fundamental concepts would be represented by symbols
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- Revised almost all areas of mathematics: filling up details, adding proofs, and arranging the whole in a consistent form
- Euler's famous equation: ei(pi)+1 = 0
- In which 'i' is the sign for the impossible square root of -1
- Solved a puzzle of how to cross seven bridges without re-crossing them by mathematically representing and formalizing it, in doing so he gave birth to modern graph theory
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- Revelled in and put on display the sheer beauty of mathematics
- The"Euler-Lagrange equation" concerns itself with paths, curves, and surfaces for which a given function has a stationary value
- Lagrangian points define a position in space where the pulls of two rotating gravitational bodies combine to form a point at which a third body of comparatively negligible mass would remain stationary
- These are valuable in positioning satellites for synchronous orbit and may enable practical interplanetary missions with less fuel
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- Mécanique Céleste (Celestial Mechanics), translated the geometrical study of mechanics by Newton to one based on calculus
- Used calculus, among other things, to explore probability theory
- Laplace's partial differential equation, often referred to as Laplace's Equation has been used for tasks as diverse as describing the stability of the solar system to the field around an electrical charge
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- Discovered that valid self-consistent geometries could be created in which Euclid's fifth parallel postulate did not hold
- These came to be known as 'non-Euclidean geometries'
- Gaussian distribution curve, referred to as 'normal distribution', is wildly applicable in experimental situations where it describes the deviations of repeated measurements from the mean
- Positive and negative deviations are equally likely, and small deviations are much more likely than large deviations
- Also known for work on primes, integers, integration, and elimination, which were named Gaussian after him
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- Regarded as the first person to anticipate the general-purpose computer and as the first "computer programmer"
- Through her acquaintance with Mary Somerville (who translated Laplace's works into English), she met Charles Babbage, the inventor of the calculating machine known as the "Difference Engine"
- Babbage later reported at a conference plans for a machine that could not only foresee but act: the "Analytical Engine"
- Lovelace translated an article written on this machine adding her own notes, which became the definitive work on computing
- When the United States DoD completed an advanced new computer language in 1980, they named it after her
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