Journey Through Genius: The Great Theorems of Mathematics Quiz | Eight Week Quiz A

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Euclid's Proof of the Pythagorean Theorem.

Multiple Choice Questions

1. What did the Pythagorean Theorem accomplish for mathematics?
(a) The concept of providing a logical proof.
(b) The concept of constructing useful mathematics.
(c) The ability to measure angles.
(d) The ability to find square roots.

2. What did Dunham consider extraordinary about the Elements?
(a) The content was totally unique.
(b) How Hippocrates ordered the book.
(c) The content was not based on previous authors' work.
(d) How geometric proofs were presented.

3. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) Circle.
(b) Intersection.
(c) 180 degree angle.
(d) Parallel lines.

4. What did Hippocrates do that advanced mathematical methods?
(a) He proved that mathematics can be applied in a unlogical order.
(b) He demonstrated that geometry does not have to be based on previous knowledge.
(c) He built theorems based on sequencially more complex proofs.
(d) He created a new ways to disprove theories.

5. What does the Pythagorean Theorem state?
(a) For any right triangle the diagonal side is equal to the sum of the legs.
(b) For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs.
(c) For any triangle the sqaured sum of the legs is equal to half the hypotenuse.
(d) For any triangle the sum of the legs squared is equal to the length of the hypotenuse.

Short Answer Questions

1. In Elements, how many postulates must be accepted as given?

2. Which of Euclid's postulates troubled many of the following generations of mathematicians?

3. Who was the first of ancient philosophers to consider why geometric properties existed?

4. What was most useful about finding the square of a shape, before Hippocrates?

5. After Hippocrates, what shape did the Greeks attempt to square without success?

(see the answer key)

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