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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. What allowed Cardano to justify publishing his book?**
**(a)** He found del Ferro's orgininal solution to the cubic. **(b)** He was dead, and the book was really published by his student. **(c)** He found Fior's documents which spoke against Tartaglia. **(d)** He was punished as a heretic,

**2. What did Euclid state about pi in Elements?**
**(a)** There is a constant relationship between the area of a circle and the square of its diameter. **(b)** There is no relationship between the area of a circle and its circumference. **(c)** The proportion of diameter to area is never equal. **(d)** The proportion of area to circumference is never equal.

**3. Heron devised which of the following methods?**
**(a)** A way to determine the volume in a sphere. **(b)** A way to determine the area of a triangle. **(c)** A way to solve binomial equations. **(d)** A way to apply mathematics to public health.

**4. Heron's work referred to the work of what other famous scholar?**
**(a)** Hippocrates. **(b)** Thales. **(c)** Euclid. **(d)** Archimedes.

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

## Short Answer Questions

**1.** What did Gauss set out to prove?

**2.** How many definitions were stated in Elements?

**3.** How do we know about Hippocrates proofs and theorems?

**4.** As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

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

## Short Essay Questions

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

**2.** Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

**3.** Who was Luca Pacioli, and what controversy was sparked over his writings?

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

**5.** Describe how Cardano eventually publishes the solution to cubic equations.

**6.** Describe the contents of Cardano's book.

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

**8.** How did Heron find the area of a triangle, and what did Dunham state about Heron's work?

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

**10.** Describe what Gauss discovered according to Dunham.

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