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### 12 Cards in this Set

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 what about the greek perspective on math was new or different? deductive reasoning notion of infinity solved problems for fun rational inquiry (from greek philosophy) more trade-oriented economic pursuits famous greek mathematicians Thales Pythagoras Aristotle Archimedes What did did Thales work on? geometry & practical applications of trig What did Thales know about triangles? similarity and congruence How did Thales figure out the height of a pyramid? Measured shadow from pyramid, shadow from straight stick (both on level ground). Then, assume similarity. Thus, hpramid/hstick = hshadowpyramid/hshadowstick What geometric statements did Thales claim and prove? 1. Circle is bisected by diameter 2. Base angles in isosceles triangle are equal 3. Vertical angles are equal 4. An angle inscribed in a semi-circle is a right angle Pythagoras was a leader with many...? Disciples. He was the first to have them. Pythagoras developed the idea of number sense. What were the two components of number sense? arithmetic - abstract relation between #s logistics - practical art of computing Pythagoras believed some weird stuff about the universe. Specifically: that integers were the fundamental organizing mechanism for the universe (oh noes irrational #s!) What were the types of numbers Pythagoras identified? 1. odd/even numbers 2. figurate numbers 2a. triangular - n(n+1)/2 2b. oblong - n(n+1) 3. friendly numbers (each is sum of the divisors of the other) 4. perfect numbers (number that is the sum of its own divisors) What type of number did Aristotle discover? Incommensurate (irrational number) What were Pythagoras's formulae for constructing Pythagorean triples? 1. if m odd, m^2 + [(m^2 -1)/2]^2 = [(m^2+1)/2]^2 2. if m either odd or even, (2m)^2 + (m^2 -1)^2 = (m^2+1)^2