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

2. Which of the following was NOT one of the basic definitions in Elements?
(a) Straight Line.
(b) Line.
(c) Parabola.
(d) Right angles.

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

4. Which of the following was an important proposition given by Euclid's number theory?
(a) Any perfect number is divisible by some composite number.
(b) Any composite number is divisible by some prime number.
(c) Any even number is divisible by 3.
(d) Numbers from one to ten are only divisible by composite numbers.

5. How did Lindeman prove his conclusion?
(a) Lindeman proved that some numbers are constructable without the use of a compass.
(b) Lindeman proved that square roots are irrational numbers.
(c) Lindeman proved that all numbers are constructable with a compass and ruler.
(d) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.

Short Answer Questions

1. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?

2. What was the bases of Hippocrates's proof ?

3. Which of the following is false about the modern implications of Euclid's number theory?

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

5. What was Hippocrates famous for?

(see the answer key)

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