# Mathematics and its History 1

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famous mathematicians and their discoveries

Pythagoras

Euclid

Diophantus

Babylonians

Descartes

Thales

Kepler

Lindemann

Gauss

Fermat primes

Euler

mersenne primes

### F(n+2) = F(n+1) + F(n)

Fibonacci sequence

Pell's equation

Archimedes

Eudoxus

Theaetus

### integer triples (a,b,c) satisfying 1, such that a^2 + b^2 = c^2, for example (3,4,5) (5,12,13) (8,15,17)

pythagorean triples

### a quantity that is not a ratio of whole numbers

irrational number

rational number

axiom

postulates

common notions

reflexive

symmetric

transitive

### a solid that is convex and has congruent shapes on each side, there are only five.

regular polyhedron

### a quantity that is not the root of any polynomial equation with rational coefficients

transcendental number

hyperbola

ellipse

parabola

prime numbers

### each natural number factors into primes in exactly one way

unique prime factorization

### a method for finding the greatest common divisor of two natural numbers, book VII

Euclidean algorithm

### a number transferred from geometric ideas to number theory

polygonal numbers

even number

odd number

perfect number

### if p is a prime number that divides ab, then p divides a or b

prime divisor property

anthyphairesis

polygon

coprime numbers

natural number

integer

### same sides and same angles, SSS SSA SAA

congruent triangles

### only have 3 angles in common

similar triangles

arithmetic

geometry

golden ratio

### duplication of the cube squaring of the circle trisection of an angle

three main problems of the ancient greeks

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