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This quiz consists of 5 multiple choice and 5 short answer questions through The Bernoullis and the Harmonic Series.
Multiple Choice Questions
1. What else, besides a solution to cubic equations, was in Cardano's book?
(a) An alegrabic solution to quintic equations,
(b) A proof of the Pythagorean Theorem.
(c) A solution to quartic equations.
(d) A suggested method to depress all complex geometry.
2. What does the Pythagorean Theorem state?
(a) For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs.
(b) For any triangle the sqaured sum of the legs is equal to half the hypotenuse.
(c) For any triangle the sum of the legs squared is equal to the length of the hypotenuse.
(d) For any right triangle the diagonal side is equal to the sum of the legs.
3. What did Archimedes manage to prove using Euclid's ideas?
(a) That the square of a diameter is equal to pi.
(b) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
(c) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.
(d) That the value of pi is proportional to the area of the circle.
4. According to Euclid, when is a triangle a right triangle?
(a) When a triangle has three sides whose squares are equal to the area of the triangle.
(b) When a triangle has a side whose square is the sum of the squares of the two legs.
(c) When a triangle can be constructed with three unequal sides.
(d) When a triangle does not have a side which can be considered a hypotenuse.
5. What did Hippocrates do that advanced mathematical methods?
(a) He created a new ways to disprove theories.
(b) He proved that mathematics can be applied in a unlogical order.
(c) He demonstrated that geometry does not have to be based on previous knowledge.
(d) He built theorems based on sequencially more complex proofs.
Short Answer Questions
1. What did Heron's advances put into historical perspective for Dunham?
2. What did British scholars accuse Leibniz of?
3. What did Dunham consider as Archimedes's "masterpiece"?
4. What great theorem is presented by Dunham in this chapter?
5. Which words best describe how solid proofs were developed in Elements?
This section contains 477 words
(approx. 2 pages at 300 words per page)