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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. How did Lindeman prove his conclusion?**
**(a)** Lindeman proved that square roots are irrational numbers. **(b)** Lindeman proved that some numbers are not constructable with only a compass and straight-edge. **(c)** Lindeman proved that some numbers are constructable without the use of a compass. **(d)** Lindeman proved that all numbers are constructable with a compass and ruler.

**2. Which of the following becomes an important definition in mathematics that was first presented in Elements?**
**(a)** Parallel line. **(b)** 180 degree angle. **(c)** Intersection. **(d)** Circle.

**3. Who wrote a treatise that supposed that cubic equations may be impossible to solve?**
**(a)** Scipione del Ferro. **(b)** Luca Pacioli. **(c)** Niccolo Fontana. **(d)** Gerolamo Cardano.

**4. Who was the first of ancient philosophers to consider why geometric properties existed?**
**(a)** Thales. **(b)** Hippocrates. **(c)** Aristotle. **(d)** Pythagoras.

**5. Which is a geometric concept that humans have been aware of since the dawn of agriculture?**
**(a)** Gravity. **(b)** Area. **(c)** Volume. **(d)** Metric system.

## Short Answer Questions

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

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

**3.** What were the proofs in Elements based on?

**4.** What was the bases of Hippocrates's proof ?

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

## Short Essay Questions

**1.** Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

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

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

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

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

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

**7.** Describe the ancient city Alexandria and name a few of its third century geniuses.

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

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

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

This section contains 894 words(approx. 3 pages at 300 words per page) |