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Name: _________________________ | Period: ___________________ |

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

**2. How many definitions were stated in Elements?**
**(a)** Twenty-three. **(b)** Five. **(c)** Eighteen. **(d)** Thirty.

**3. 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 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 neither greater than nor less than the area of the triangle and therefore must be equal to it.

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

**5. What did Plato use his inspiration from Euclid for?**
**(a)** To construct his theory on the shape of the Universe. **(b)** To create a new theorem of algebra. **(c)** To prove Euclid's number theory was incorrect. **(d)** To classify geometric shapes by their complexity.

## Short Answer Questions

**1.** After Hippocrates, what shape did the Greeks attempt to square without success?

**2.** What range of values did Archimedes determine for pi?

**3.** Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

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

**5.** What shape was NOT demonstrated in the Elements as having a relationship to other shapes?

## Short Essay Questions

**1.** What did Dunham describe in the epilogue of the chapter?

**2.** Describe the events that follow del Ferro's death between Fior and Tartaglia.

**3.** Explain when the knowledge of ancient scholars was rediscovered.

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

**5.** Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

**6.** Describe who was Archimedes and how Dunham described his character.

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

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

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

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

This section contains 900 words(approx. 3 pages at 300 words per page) |