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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. According to Euclid, when is a triangle a right triangle?**
**(a)** When a triangle can be constructed with three unequal sides. **(b)** When a triangle does not have a side which can be considered a hypotenuse. **(c)** When a triangle has three sides whose squares are equal to the area of the triangle. **(d)** When a triangle has a side whose square is the sum of the squares of the two legs.

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

**3. What did Dunham discuss for many pages in this chapter?**
**(a)** Heron's complicated proof. **(b)** Heron's political tendancy. **(c)** Heron's origins of the universe. **(d)** Heron's religious beliefs-

**4. What did the Pythagorean Theorem accomplish for mathematics?**
**(a)** The concept of providing a logical proof. **(b)** The ability to measure angles. **(c)** The ability to find square roots. **(d)** The concept of constructing useful mathematics.

**5. Which mathematician was first to take the challenge to solve cubic equations?**
**(a)** Tartaglia. **(b)** Niccolo Fontana. **(c)** Luca Pacioli. **(d)** Scipione del Ferro.

## Short Answer Questions

**1.** Which of the following best describes Archimedes as discussed by Dunham?

**2.** What did Dunham consider as Archimedes's "masterpiece"?

**3.** Which is a geometric concept that humans have been aware of since the dawn of agriculture?

**4.** Which of the following is true about pi, as described by Dunham.

**5.** Besides being a mathematician, what else other work was Archimedes famous for?

## Short Essay Questions

**1.** Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

**2.** Describe Euclid's postulates and notions in how they were important in constructing his proofs.

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

**4.** Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

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

**6.** What did Dunham explain about the shift in learning from the West to the East?

**7.** What was already known about circles before Archimedes?

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

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

**10.** 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.

This section contains 946 words(approx. 4 pages at 300 words per page) |