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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. Which of Euclid's postulates troubled many of the following generations of mathematicians?**
**(a)** Euclid's postulate on parallel lines. **(b)** Euclid's postulate on right triangles. **(c)** Euclid's postulate on creating an arc. **(d)** Euclid's proof on right triangles.

**2. What allowed Cardano to justify publishing his book?**
**(a)** He was punished as a heretic, **(b)** He was dead, and the book was really published by his student. **(c)** He found Fior's documents which spoke against Tartaglia. **(d)** He found del Ferro's orgininal solution to the cubic.

**3. Which city was the center of thinking and learning in Third century BC?**
**(a)** Athens. **(b)** Rome. **(c)** Olympia. **(d)** Alexandria.

**4. Which of the following was NOT one of the basic definitions in Elements?**
**(a)** Line. **(b)** Straight Line. **(c)** Right angles. **(d)** Parabola.

**5. What did Dunham consider extraordinary about the Elements?**
**(a)** The content was not based on previous authors' work. **(b)** How geometric proofs were presented. **(c)** The content was totally unique. **(d)** How Hippocrates ordered the book.

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

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

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

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

**10. What was Euclid's definition of a prime number?**
**(a)** Numbers which do not, and can not, contain a perfect number. **(b)** Numbers which can only be divided by themselves and 1. **(c)** Numbers which are divisible by 2. **(d)** Numbers which contain an infinite number of composite numbers.

**11. 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.

**12. Who was Heron?**
**(a)** A philosopher from Greece. **(b)** A matematician from Alexanderia. **(c)** A politician from Rome. **(d)** A physician from the far East.

**13. Which of the following is an example of a postulate that must be accepted in Elements?**
**(a)** It is possible to connect any two points with a line and make a circle. **(b)** It is possible to draw an arc with any three points. **(c)** It is possible to draw a circle that contains no lines. **(d)** It is possible to draw a straight line between an infinite number of points.

**14. What were the proofs in Elements based on?**
**(a)** Basic definitions. **(b)** Ancient greek geometry. **(c)** Novel notions. **(d)** Lindeman's method.

**15. Where was Archimedes born?**
**(a)** Rome. **(b)** Olympia. **(c)** Athens. **(d)** Sicily.

## Short Answer Questions

**1.** Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

**2.** Heron devised which of the following methods?

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

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

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

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