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

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Euclid's Proof of the Pythagorean Theorem.

Multiple Choice Questions

1. Which is one of the common notions presented in Elements?
(a) "Things with are equal have an inverse that is equal."
(b) "The inverse of a line makes a circle."
(c) "Things which are equal to the same thing are also equal to each other."
(d) "Points with equal values can be connected with a line of equal value."

2. What instruments did the Greeks use to square a shape?
(a) A sphere and ruler.
(b) A compass and a ruled straight-edge.
(c) A pendulum.
(d) A small grid.

3. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?
(a) Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs.
(b) Euclid constructed squares on the sides of right triangles.
(c) Euclid used his own axioms and propositions to show relationships,
(d) Euclid used propositions about similar angles and parallel lines.

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

5. Which of the following becomes an important definition in mathematics that was first presented in Elements?
(a) Parallel line.
(b) Circle.
(c) 180 degree angle.
(d) Intersection.

Short Answer Questions

1. What did Hippocrates do that advanced mathematical methods?

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

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

4. What was true about Hippocrates's proof?

5. What did Euclid do in his 48th proposition?

(see the answer key)

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