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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. Dunham showed that Heron's proof could also be used as which of the following?
(a) A proof of Hippocrates' squared areas.
(b) A proof of Euclid's number theory
(c) A proof of the Pythagorean Theorem.
(d) A proof of Archimedes' number theory.

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

3. What did Ferdinand Lindeman prove in 1882?
(a) It is impossible to find the square of a semicircle.
(b) That the square root of the hypotenuse of a right triangle can not be found.
(c) That the square of a circle can not be found with a compass and a straight-edge.
(d) It is possible to find the square of a circle.

4. Which of the following was one of Euclid's great theorems?
(a) There exists an infinite number of prime numbers.
(b) Prime numbers are more comples than discrete numbers.
(c) There exists an finite number of prime numbers.
(d) There exists only infinite and whole numbers.

5. Which of the following best describes Archimedes as discussed by Dunham?
(a) Creative but stubborn.
(b) Loud and arrogant.
(c) Absent-minded genius.
(d) Mild-mannered researcher.

6. Which of the following is true in modern math about twin primes?
(a) They are infinite.
(b) They are not considered whole numbers.
(c) We don't know if they are finite or infinite.
(d) Their sum is always another prime number.

7. After Hippocrates, what shape did the Greeks attempt to square without success?
(a) Parallelogram.
(b) Circle.
(c) Hemisphere.
(d) Pentagon.

8. In what century did Archimedes live?
(a) Twelthf century A.D.
(b) Third century B.C.
(c) Nineteeth century A.D.
(d) First century A.D,

9. 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 constructed squares on the sides of right triangles.
(c) Euclid used his own axioms and propositions to show relationships,
(d) Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs.

10. Which of the following was NOT defined by Euclid?
(a) Nominal numbers.
(b) Odd numbers.
(c) Whole numbers.
(d) Even numbers.

11. How did Archimedes demonstrate his theory of pi?
(a) He demonstrated that the area of the circle is always greater than the area of the triangle.
(b) He demonstrated that the area of the circle is never equal to the area of the triangle.
(c) He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it.
(d) He demonstrated that the area of the circle is never less than the area of the triangle.

12. Who was the author of the book Elements?
(a) Lindemann.
(b) Hippocrates.
(c) Euclid.
(d) Einstein.

13. What is true about prime numbers?
(a) Prime numbers can never be an odd number.
(b) Prime numbers can not exist in a finite series.
(c) That for every group of prime numbers, there exists at least one more prime.
(d) Prime numbers are not divisible by other numbers.

14. That properties of specific shapes were early Egyptians aware of?
(a) Pi and the diameter of a circle.
(b) Right triangles.
(c) Parallelograms.
(d) Irregular solids.

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

Short Answer Questions

1. Where was Archimedes born?

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

3. What was most useful about finding the square of a shape, before Hippocrates?

4. What did Dunham consider extraordinary about the Elements?

5. Which of the following was an important proposition given by Euclid's number theory?

(see the answer keys)

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