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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. What did Euclid do in his 48th proposition?**
**(a)** Euclid demonstrated the faults of the Pythagorean Theorem. **(b)** Euclid demonstrated how to use the Pythagorean Theorem. **(c)** Euclid proved the Pythagorean Theorem. **(d)** Euclid proved the converse of the Pythagorean Theorem.

**2. What was the bases of Hippocrates's proof ?**
**(a)** Properties of points and lines. **(b)** Properties of area to volume measurements. **(c)** Properties of triangles and semicircles. **(d)** Properties of squares and cubes.

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

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

**5. After working on pi, what did Archimedes continue with in his study of mathematics?**
**(a)** He studied the relationship between ratios in triangles. **(b)** He studied the relationship of sine to cosine. **(c)** He studied the volume and surface area of spheres, cones, and cylinders. **(d)** He studied the volume to surface area ratios of cubes.

**6. How many definitions were stated in Elements?**
**(a)** Eighteen. **(b)** Five. **(c)** Twenty-three. **(d)** Thirty.

**7. 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.

**8. Who challenged Tartaglia to a contest to solve cubic equations?**
**(a)** Fior. **(b)** Cardano. **(c)** del Ferro. **(d)** Pacioli.

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

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

**11. Why did Cardano take an oath to secrecy?**
**(a)** It was the only way to get Tartaglia's solution to cubic equations. **(b)** It was to the only way to win the contest with Fior, **(c)** It was the only way to get his book published. **(d)** It was the only way he could become a priest,

**12. What else, besides a solution to cubic equations, was in Cardano's book?**
**(a)** An alegrabic solution to quintic equations, **(b)** A solution to quartic equations. **(c)** A proof of the Pythagorean Theorem. **(d)** A suggested method to depress all complex geometry.

**13. After Hippocrates, what shape did the Greeks attempt to square without success?**
**(a)** Parallelogram. **(b)** Hemisphere. **(c)** Circle. **(d)** Pentagon.

**14. How did Lindeman prove his conclusion?**
**(a)** Lindeman proved that some numbers are not constructable with only a compass and straight-edge. **(b)** Lindeman proved that some numbers are constructable without the use of a compass. **(c)** Lindeman proved that square roots are irrational numbers. **(d)** Lindeman proved that all numbers are constructable with a compass and ruler.

**15. What instruments did the Greeks use to square a shape?**
**(a)** A sphere and ruler. **(b)** A compass and a ruled straight-edge. **(c)** A pendulum. **(d)** A small grid.

## Short Answer Questions

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

**2.** What did the Pythagorean Theorem accomplish for mathematics?

**3.** Which city was the center of thinking and learning in Third century BC?

**4.** Which of the following is an example of a perfect number?

**5.** What does the Pythagorean Theorem state?

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