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Ancient Math Pioneers: Thales and Pythagoras

Explore the mathematical contributions of Thales and Pythagoras from 800-336 BC. Thales introduced key geometric principles like triangle congruence and circle theorems. Pythagoras founded a school centered on numbers, with focus on the Pythagorean Theorem and special number properties.

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Ancient Math Pioneers: Thales and Pythagoras

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  1. Demonstrative Math800 - 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.

  2. Thales (continued) • The vertical angles formed by two intersecting lies are equal. • Any angle inscribed in a semicircle is a right angle.

  3. Thales Anecdote 1 Olive oil press

  4. Thales Anecdote 2 Mule with salt

  5. Thales anecdote 3 Marriage

  6. Pythagoras ( 570-500 BC)

  7. 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

  8. Pythagorean Arithmetic • Amicable numbers • Two numbers such that each is the sum of the proper divisors of the other • 284,220

  9. Pythagorean Arithmetic • Perfect numbers • Number is equal to the sum of its proper divisors • 6,28,496

  10. Pythagorean Arithmetic • Deficient numbers • Number exceeds the sum of its divisors • 8

  11. Pythagorean Arithmetic • Abundant numbers • Number is less than the sum of its proper divisors • 12

  12. Figurate numbers • Triangular numbers

  13. Figurate numbers • Square numbers

  14. Figurate numbers • Pentagonal numbers

  15. Irrational Magnitudes • Rational numbers • Number line • Irrational numbers • Square root of 2 • Mortal blow to Pythagorean philosophy

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