*BookRags*. (c)2015 BookRags, Inc. All rights reserved.

Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

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

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

**3. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?**
**(a)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter. **(b)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference. **(c)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference. **(d)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.

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

**5. Which of the following was one of Euclid's great theorems?**
**(a)** There exists an infinite number of prime numbers. **(b)** There exists only infinite and whole numbers. **(c)** There exists an finite number of prime numbers. **(d)** Prime numbers are more comples than discrete numbers.

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

**7. Which of the following were an example of twin primes?**
**(a)** 15 and 16. **(b)** 19 and 22. **(c)** 11 and 13. **(d)** 2 and 6.

**8. Which of the following is an example of a perfect number?**
**(a)** 1. **(b)** 20. **(c)** 6. **(d)** 10.

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

**10. Heron's work referred to the work of what other famous scholar?**
**(a)** Archimedes. **(b)** Euclid. **(c)** Hippocrates. **(d)** Thales.

**11. 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 logically square all the factors in a cubic equation. **(d)** A method to solve equations with two variables.

**12. What did Heron's advances put into historical perspective for Dunham?**
**(a)** A shift in learning across continents. **(b)** A change in learning foundations in the ancient scholarly universities. **(c)** A change in political theory across the globe. **(d)** A shift in information flow that ignored socioeconomic order.

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

**14. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?**
**(a)** Euclid used propositions about similar angles and parallel lines. **(b)** Euclid constructed squares on the sides of right triangles. **(c)** Euclid used his own axioms and propositions to show relationships, **(d)** Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs.

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

## Short Answer Questions

**1.** Which words best describe how solid proofs were developed in Elements?

**2.** When was the work of these early thinkers rediscovered again in history?

**3.** What was most useful about finding the square of a shape, before Hippocrates?

**4.** What did most of Heron's work deal with?

**5.** What did Dunham claim about Archimedes's determination of a number value for pi?

This section contains 801 words(approx. 3 pages at 300 words per page) |