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

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Archimedes' Determination of Circular Area.

Multiple Choice Questions

1. 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 diameter and the other leg equal to the circle's circumference.
(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 diameter.
(c) 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.
(d) 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.

2. Which of the following was one of Euclid's great theorems?
(a) There exists an finite number of prime numbers.
(b) There exists an infinite number of prime numbers.
(c) There exists only infinite and whole numbers.
(d) Prime numbers are more comples than discrete numbers.

3. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?
(a) Quadrature.
(b) Triangulation.
(c) Square root.
(d) Cubation.

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

5. How many sides did the pentadecagon have, as presented by Euclid?
(a) Five.
(b) Ten.
(c) Twenty.
(d) Fifteen.

Short Answer Questions

1. Which was true of Euclid's number theory?

2. How did Lindeman prove his conclusion?

3. That properties of specific shapes were early Egyptians aware of?

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

5. Which of the following was NOT defined by Euclid?

(see the answer key)

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