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

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

Multiple Choice Questions

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

2. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?
(a) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter.
(b) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.
(c) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.
(d) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.

3. 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 right triangle the diagonal side is equal to the sum of the 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.

4. What did Dunham discuss for many pages in this chapter?
(a) Heron's complicated proof.
(b) Heron's religious beliefs-
(c) Heron's political tendancy.
(d) Heron's origins of the universe.

5. Which of the following is false about the modern implications of Euclid's number theory?
(a) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.
(b) Whether there are no odd perfect numbers is still not known.
(c) Euclid's recipe for constructing even perfect numbers is incorrect.
(d) Euclid gave a good idea for how to construct even perfect numbers.

Short Answer Questions

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

2. In what century did Archimedes live?

3. What was Euclid's definition of a prime number?

4. What was true about Hippocrates's proof?

5. Heron's work referred to the work of what other famous scholar?

(see the answer key)

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