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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. Heron devised which of the following methods?**
**(a)** A way to apply mathematics to public health. **(b)** A way to solve binomial equations. **(c)** A way to determine the volume in a sphere. **(d)** A way to determine the area of a triangle.

**2. Who was del Ferro's student?**
**(a)** Gerolamo Cardano. **(b)** Luca Pacioli. **(c)** Antonio Fior. **(d)** Niccolo Fontana.

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

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

**5. In general, what did Euclid's number theory describe?**
**(a)** The relationship of decimals to integers. **(b)** The nature of whole numbers. **(c)** The nature of measuring geometry. **(d)** The relationship of fractions to decimals.

**6. When was the work of these early thinkers rediscovered again in history?**
**(a)** In the 20th century. **(b)** In the 18th century. **(c)** In the Elizabethian age. **(d)** In the Renaissance.

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

**8. What provided most of the content in the book Elements?**
**(a)** Postulates. **(b)** Propositions. **(c)** Hypotheses. **(d)** Notions.

**9. Which of the following is false about the modern implications of Euclid's number theory?**
**(a)** Euclid's recipe for constructing even perfect numbers is incorrect. **(b)** Great mathematicians continue to puzzle over some aspects of Euclid's number theory. **(c)** Euclid gave a good idea for how to construct even perfect numbers. **(d)** Whether there are no odd perfect numbers is still not known.

**10. What was true about Hippocrates's proof?**
**(a)** It was fairly easy and simple. **(b)** The proof was exceedingly difficult and not understood at the time. **(c)** The proof was easy if their was advanced technology available. **(d)** It was useful for circles.

**11. Who was the first of ancient philosophers to consider why geometric properties existed?**
**(a)** Pythagoras. **(b)** Thales. **(c)** Hippocrates. **(d)** Aristotle.

**12. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?**
**(a)** Parallel lines. **(b)** Circle. **(c)** 180 degree angle. **(d)** Intersection.

**13. Which of the following is true in modern math about twin primes?**
**(a)** They are not considered whole numbers. **(b)** Their sum is always another prime number. **(c)** We don't know if they are finite or infinite. **(d)** They are infinite.

**14. 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.

**15. Which words best describe how solid proofs were developed in Elements?**
**(a)** Axiomatic framework. **(b)** Programmed order. **(c)** Simple arguments. **(d)** Inverted scaffold.

## Short Answer Questions

**1.** Which of the following becomes an important definition in mathematics that was first presented in Elements?

**2.** Who was the author of the book Elements?

**3.** What did Gauss set out to prove?

**4.** What was the title of Cardano's book which contained the solution to the cubic?

**5.** What did Apollonius work with in mathematics?

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