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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 did Archimedes manage to prove using Euclid's ideas?**
**(a)** That the relationship of area to circumference is really the same as the relationship of radius to diameter. **(b)** That the value of pi is proportional to the area of the circle. **(c)** That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference. **(d)** That the square of a diameter is equal to pi.

**2. How many sides did the pentadecagon have, as presented by Euclid?**
**(a)** Ten. **(b)** Fifteen. **(c)** Twenty. **(d)** Five.

**3. What did Hippocrates do that advanced mathematical methods?**
**(a)** He created a new ways to disprove theories. **(b)** He demonstrated that geometry does not have to be based on previous knowledge. **(c)** He proved that mathematics can be applied in a unlogical order. **(d)** He built theorems based on sequencially more complex proofs.

**4. Which of Euclid's postulates troubled many of the following generations of mathematicians?**
**(a)** Euclid's proof on right triangles. **(b)** Euclid's postulate on right triangles. **(c)** Euclid's postulate on creating an arc. **(d)** Euclid's postulate on parallel lines.

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

## Short Answer Questions

**1.** What was true about Heron's theorem as described by Dunham?

**2.** Heron's work referred to the work of what other famous scholar?

**3.** Exactly what limit is reached at a quartic equation?

**4.** Who was the first of ancient philosophers to consider why geometric properties existed?

**5.** As described by Archimedes, what is always true about he diameter of the circle?

## Short Essay Questions

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

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

**3.** Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

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

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

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

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

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

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

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

This section contains 975 words(approx. 4 pages at 300 words per page) |