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

2. How did Archimedes demonstrate his theory of pi?
(a) 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.
(b) He demonstrated that the area of the circle is never less than the area of the triangle.
(c) He demonstrated that the area of the circle is never equal to the area of the triangle.
(d) He demonstrated that the area of the circle is always greater than the area of the triangle.

3. According to Euclid, when is a triangle a right triangle?
(a) When a triangle has three sides whose squares are equal to the area of the triangle.
(b) When a triangle has a side whose square is the sum of the squares of the two legs.
(c) When a triangle can be constructed with three unequal sides.
(d) When a triangle does not have a side which can be considered a hypotenuse.

4. Who challenged Tartaglia to a contest to solve cubic equations?
(a) del Ferro.
(b) Cardano.
(c) Fior.
(d) Pacioli.

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

Short Answer Questions

1. Besides being a mathematician, what else other work was Archimedes famous for?

2. Heron's work referred to the work of what other famous scholar?

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

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

5. What did Plato use his inspiration from Euclid for?

Short Essay Questions

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

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

3. Describe the contents of Cardano's book.

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

5. According the Dunham, how did Euclid prove his theory on the infinitude of primes?

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

7. Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.

8. Describe who was Archimedes and how Dunham described his character.

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

10. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

(see the answer keys)

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