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12 Cards in this Set
- Front
- Back
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what about the greek perspective on math was new or different?
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deductive reasoning
notion of infinity solved problems for fun rational inquiry (from greek philosophy) more trade-oriented economic pursuits |
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famous greek mathematicians
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Thales
Pythagoras Aristotle Archimedes |
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What did did Thales work on?
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geometry & practical applications of trig
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What did Thales know about triangles?
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similarity and congruence
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How did Thales figure out the height of a pyramid?
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Measured shadow from pyramid, shadow from straight stick (both on level ground).
Then, assume similarity. Thus, hpramid/hstick = hshadowpyramid/hshadowstick |
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What geometric statements did Thales claim and prove?
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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 |
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Pythagoras was a leader with many...?
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Disciples. He was the first to have them.
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Pythagoras developed the idea of number sense. What were the two components of number sense?
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arithmetic - abstract relation between #s
logistics - practical art of computing |
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Pythagoras believed some weird stuff about the universe. Specifically:
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that integers were the fundamental organizing mechanism for the universe (oh noes irrational #s!)
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What were the types of numbers Pythagoras identified?
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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) |
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What type of number did Aristotle discover?
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Incommensurate (irrational number)
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What were Pythagoras's formulae for constructing Pythagorean triples?
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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 |
