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Name: _________________________ | Period: ___________________ |

This test consists of 15 multiple choice questions and 5 short answer questions.

## Multiple Choice Questions

**1. In what century did Archimedes live?**
**(a)** First century A.D, **(b)** Twelthf century A.D. **(c)** Third century B.C. **(d)** Nineteeth century A.D.

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

**3. Who asked Tartaglia for his solution to cubic equations?**
**(a)** Fontana. **(b)** Cardano. **(c)** Fior, **(d)** Pacioli.

**4. Which of the following is true about pi, as described by Dunham.**
**(a)** The measurement of pi was redetermined after Archimedes's death. **(b)** The measurement of pi should not have been so difficult for Archimedes to demonstrate. **(c)** The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics. **(d)** The measurement of pi is a challenge that continues into modern mathematics.

**5. Where did Hippocrates come from?**
**(a)** Rome. **(b)** Athens. **(c)** Chios. **(d)** Constinople.

**6. Where was Neil's Abel from?**
**(a)** Ireland. **(b)** Finland. **(c)** Great Britian, **(d)** Norway.

**7. Exactly what limit is reached at a quartic equation?**
**(a)** The limit of logical geometric proofs. **(b)** The limit of the decompressed cubic method. **(c)** The limit of algebra. **(d)** The limit of the Pythagorean Theorem.

**8. Which of the following could NOT be included as a step in Euclid's great theorem?**
**(a)** After summation, the new number can be prime or composite. **(b)** Take a finite group of primes and add them together, plus one. **(c)** If a new number is found to be composite, then it must have some prime as a divisor. **(d)** Divide a infinite group of primes by the sum of their composites.

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

**10. How did Archimedes demonstrate his theory of pi?**
**(a)** He demonstrated that the area of the circle is never equal to the area of the triangle. **(b)** He demonstrated that the area of the circle is always greater than the area of the triangle. **(c)** He demonstrated that the area of the circle is never less than the area of the triangle. **(d)** He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it.

**11. Which of the following was an important proposition given by Euclid's number theory?**
**(a)** Any even number is divisible by 3. **(b)** Numbers from one to ten are only divisible by composite numbers. **(c)** Any perfect number is divisible by some composite number. **(d)** Any composite number is divisible by some prime number.

**12. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?**
**(a)** Quadrature. **(b)** Cubation. **(c)** Triangulation. **(d)** Square root.

**13. In what time period did mathematicians find a solution to cubic equations?**
**(a)** Seventeeth century. **(b)** Twentieth century. **(c)** Fifteen century. **(d)** Thirteenth century.

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

**15. Which of the following was NOT one of Gauss' discoveries?**
**(a)** That angles in a triangles can not add up to more than 180 degrees. **(b)** That under Euclid's definition parallel lines can intersect. **(c)** "Non-euclidean" geometry. **(d)** That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.

## Short Answer Questions

**1.** What was Hippocrates famous for?

**2.** What else, besides a solution to cubic equations, was in Cardano's book?

**3.** Which is one of the common notions presented in Elements?

**4.** What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

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

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