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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. Which of the following could NOT be included as a step in Euclid's great theorem?
(a) Take a finite group of primes and add them together, plus one.
(b) If a new number is found to be composite, then it must have some prime as a divisor.
(c) Divide a infinite group of primes by the sum of their composites.
(d) After summation, the new number can be prime or composite.

2. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?
(a) Euclid used propositions about similar angles and parallel lines.
(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 constructed squares on the sides of right triangles.
(d) Euclid used his own axioms and propositions to show relationships,

3. What does the Pythagorean Theorem state?
(a) For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs.
(b) For any triangle the sqaured sum of the legs is equal to half the hypotenuse.
(c) For any triangle the sum of the legs squared is equal to the length of the hypotenuse.
(d) For any right triangle the diagonal side is equal to the sum of the legs.

4. Which was true of Euclid's number theory?
(a) It was proven to the true by Hippocrates.
(b) It was incorrect, as proved by Plato.
(c) It has been proven too basic to be useful.
(d) It has an impact on modern math.

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

Short Answer Questions

1. What did Dunham consider extraordinary about the Elements?

2. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?

3. What instruments did the Greeks use to square a shape?

4. Which of the following becomes an important definition in mathematics that was first presented in Elements?

5. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

(see the answer key)

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