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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. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?**
**(a)** Cubation. **(b)** Quadrature. **(c)** Square root. **(d)** Triangulation.

**2. Which of the following was NOT one of Gauss' discoveries?**
**(a)** That under Euclid's definition parallel lines can intersect. **(b)** "Non-euclidean" geometry. **(c)** That angles in a triangles can not add up to more than 180 degrees. **(d)** That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.

**3. What did Euclid do in his 48th proposition?**
**(a)** Euclid proved the Pythagorean Theorem. **(b)** Euclid proved the converse of the Pythagorean Theorem. **(c)** Euclid demonstrated how to use the Pythagorean Theorem. **(d)** Euclid demonstrated the faults of the Pythagorean Theorem.

**4. Where did Hippocrates come from?**
**(a)** Constinople. **(b)** Chios. **(c)** Athens. **(d)** Rome.

**5. What was the same about Apollonius and Erosthanes?**
**(a)** They both studied the Universe. **(b)** They both calculated the circumference of the earth. **(c)** They were both born in the same year. **(d)** They were both mathematicians.

## Short Answer Questions

**1.** Who asked Tartaglia for his solution to cubic equations?

**2.** What did Dunham discuss for many pages in this chapter?

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

**4.** What else, besides a solution to cubic equations, was in Cardano's book?

**5.** How many sides did the pentadecagon have, as presented by Euclid?

## Short Essay Questions

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

**2.** Describe Lindeman's work on the square of a circle, and state what he discovered.

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

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

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

**6.** What did Euclid state for his theory on prime numbers?

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

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

**9.** Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

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

This section contains 917 words(approx. 4 pages at 300 words per page) |