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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