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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

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

2. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?
(a) The area of a triangle is one half the base times the height.
(b) Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr².
(c) Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference.
(d) Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference.

3. Which mathematician was first to take the challenge to solve cubic equations?
(a) Tartaglia.
(b) Luca Pacioli.
(c) Scipione del Ferro.
(d) Niccolo Fontana.

4. Who was del Ferro's student?
(a) Niccolo Fontana.
(b) Luca Pacioli.
(c) Gerolamo Cardano.
(d) Antonio Fior.

5. What did Ferdinand Lindeman prove in 1882?
(a) It is possible to find the square of a circle.
(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 impossible to find the square of a semicircle.

Short Answer Questions

1. How do we know about Hippocrates proofs and theorems?

2. Which of the following is true in modern math about twin primes?

3. Which of the following best describes Cardano's character?

4. Heron devised which of the following methods?

5. In what century did Archimedes live?

Short Essay Questions

1. Describe what the Egyptians knew about geometry and triangles before Hippocrates.

2. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

3. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

4. Describe the contents of Cardano's book.

5. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

6. What did Dunham describe in the epilogue of the chapter?

7. Describe how Cardano eventually publishes the solution to cubic equations.

8. How many definitions were in Euclid's book? List some of the definitions he included.

9. Describe what is quadrature and why it was useful in the time of Hippocrates.

10. Who was Heron, and what is known about him today?

(see the answer keys)

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