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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).

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Demonstrative Math 800 - 336 BC

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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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