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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 was Eratosthanes most famous for?**
**(a)** He showed that there are no even prime numbers. **(b)** He developed a simple way to find prime numbers and for determining the circumference of the Earth. **(c)** He developed a way to navigate using logitude and latitude. **(d)** He showed that the Earth must be a sphere.

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

**3. What did Dunham consider extraordinary about the Elements?**
**(a)** How Hippocrates ordered the book. **(b)** The content was totally unique. **(c)** The content was not based on previous authors' work. **(d)** How geometric proofs were presented.

**4. What was the bases of Hippocrates's proof ?**
**(a)** Properties of triangles and semicircles. **(b)** Properties of points and lines. **(c)** Properties of squares and cubes. **(d)** Properties of area to volume measurements.

**5. Which of the following is an example of a postulate that must be accepted in Elements?**
**(a)** It is possible to connect any two points with a line and make a circle. **(b)** It is possible to draw a straight line between an infinite number of points. **(c)** It is possible to draw an arc with any three points. **(d)** It is possible to draw a circle that contains no lines.

## Short Answer Questions

**1.** Which of the following was NOT one of Gauss' discoveries?

**2.** When was the work of these early thinkers rediscovered again in history?

**3.** What did Plato use his inspiration from Euclid for?

**4.** Which of the following was one of Euclid's great theorems?

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

## Short Essay Questions

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

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

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

**4.** Explain what Neils Abel proved.

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

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

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

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

This section contains 965 words(approx. 4 pages at 300 words per page) |