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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 is a "depressed cubic"?**
**(a)** A method to simplify measuring complex geometric forms. **(b)** A method to simpify the x squared value in a cubic equation. **(c)** A method to solve equations with two variables. **(d)** A method to logically square all the factors in a cubic equation.

**2. Besides being a mathematician, what else other work was Archimedes famous for?**
**(a)** Inventor and scientist. **(b)** Politician. **(c)** Doctor and writer, **(d)** Artist and musician.

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

**4. Who was Neil's Abel?**
**(a)** He demonstrated the modern version of the Pythagorean Theorem. **(b)** He proved that quintic equations cannot be solved using algebra. **(c)** He demonstrated that Cardano's solution to the cubic was incorrect, **(d)** He proved that to solve a quartic equation, one must use more than algebra.

**5. What did Dunham claim about Archimedes's determination of a number value for pi?**
**(a)** Archimedes's number could have been better if he had understood Euclid's work better, **(b)** Archimedes's number was not very accurate, considering the technology of his time. **(c)** Archimedes's number was perfectly correct. **(d)** Archimedes's number was very good, considering he did not have a way to calculate square roots.

## Short Answer Questions

**1.** Who was del Ferro's student?

**2.** What is true about prime numbers?

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

**4.** What is the name for determining the area of an enclosed space by constructing a square of equivalent area?

**5.** How did Archimedes demonstrate his theory of pi?

## Short Essay Questions

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

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

**3.** Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

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

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

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

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

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

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

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

This section contains 951 words(approx. 4 pages at 300 words per page) |