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. In Elements, how many postulates must be accepted as given?
(a) Twelve,
(b) Twenty-two.
(c) Eighteen.
(d) Five.

2. Which of the following was NOT one of Gauss' discoveries?
(a) "Non-euclidean" geometry.
(b) That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.
(c) That angles in a triangles can not add up to more than 180 degrees.
(d) That under Euclid's definition parallel lines can intersect.

3. Which of the following is an example of a perfect number?
(a) 10.
(b) 6.
(c) 1.
(d) 20.

4. Who was Eratosthanes?
(a) He was the chief librarian, and a mathematician.
(b) He was a mathematician, and leading doctor.
(c) He was a teacher and philosopher.
(d) He was the first to study political sciences.

5. Which words best describe how solid proofs were developed in Elements?
(a) Axiomatic framework.
(b) Programmed order.
(c) Inverted scaffold.
(d) Simple arguments.

Short Answer Questions

1. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?

2. What did Archimedes manage to prove using Euclid's ideas?

3. According to Euclid, when is a triangle a right triangle?

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

5. Which of the following is an example of a postulate that must be accepted in Elements?

(see the answer key)

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