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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. What did Ferdinand Lindeman prove in 1882?
(a) That the square root of the hypotenuse of a right triangle can not be found.
(b) It is impossible to find the square of a semicircle.
(c) That the square of a circle can not be found with a compass and a straight-edge.
(d) It is possible to find the square of a circle.

2. In what century did Archimedes live?
(a) Twelthf century A.D.
(b) First century A.D,
(c) Third century B.C.
(d) Nineteeth century A.D.

3. Which of the following was NOT true about Archimedes, according to Dunham?
(a) He died as a soldier.
(b) He died during the fall of Syracuse.
(c) Archimedes died because he refused to follow orders until he completed a math problem.
(d) His death was described as being by the hands of a Roman invader.

4. What did Gauss set out to prove?
(a) That Euclid's postulate on straight lines was incorrect.
(b) That the sum of the angles in a triangle is 180 degrees.
(c) That a right angle is always equal to 90 degrees.
(d) That a circle can have less than 360 degrees.

5. Where did Hippocrates come from?
(a) Constinople.
(b) Chios.
(c) Athens.
(d) Rome.

Short Answer Questions

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

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

3. What range of values did Archimedes determine for pi?

4. How do we know about Hippocrates proofs and theorems?

5. Which of the following is an example of a perfect number?

(see the answer key)

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