Transcript Demonstrative Math 800 - 336 BC

Demonstrative Math
800 - 336 BC
Thales
A circle is bisected by any diameter
The base angles of an isosceles triangle are
equal
Two triangles are congruent if they have two
angles and one side in each respectfully
equal.
Thales (continued)
The vertical angles formed by two
intersecting lies are equal.
Any angle inscribed in a semicircle is a
right angle.
Thales Anecdote 1
Olive oil press
Thales Anecdote 2
Mule with salt
Thales anecdote 3
Marriage
Pythagoras ( 570-500 BC)
Pythagoras ( 570-500 BC)
Pythagorean Theorem
Founded Pythagorean School
Brotherhood
Whole number is the cause of various
qualities of man and matter
Exaltation and study of numbers
Pythagorean Arithmetic
Amicable numbers
Two numbers such that each is the sum of
the proper divisors of the other
284,220
Pythagorean Arithmetic
Perfect numbers
Number is equal to the sum of its proper
divisors
6,28,496
Pythagorean Arithmetic
Deficient numbers
Number exceeds the sum of its divisors
8
Pythagorean Arithmetic
Abundant numbers
Number is less than the sum of its proper
divisors
12
Figurate numbers
Triangular numbers
Figurate numbers
Square numbers
Figurate numbers
Pentagonal numbers
Irrational Magnitudes
Rational numbers
Number line
Irrational numbers
Square root of 2
Mortal blow to Pythagorean philosophy