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

2. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to draw an arc with any three points.
(b) It is possible to draw a straight line between an infinite number of points.
(c) It is possible to connect any two points with a line and make a circle.
(d) It is possible to draw a circle that contains no lines.

3. 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.

4. How do we know about Hippocrates proofs and theorems?
(a) Mathematicians rewrote all of his proofs after his death,
(b) What is known from archived documents of his time.
(c) His books and publications.
(d) What we know is from references of later mathematicians.

5. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on parallel lines.
(b) Euclid's postulate on right triangles.
(c) Euclid's proof on right triangles.
(d) Euclid's postulate on creating an arc.

Short Answer Questions

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

2. How many definitions were stated in Elements?

3. What did Ferdinand Lindeman prove in 1882?

4. What did Dunham consider extraordinary about the Elements?

5. What provided most of the content in the book Elements?

(see the answer key)

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