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

## Multiple Choice Questions

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

**2. What range of values did Archimedes determine for pi?**
**(a)** Between 3 10/11 and 3 1/7. **(b)** Between 3 and 3 1/2. **(c)** Between 3 1/2 and 3 5/8. **(d)** Between 3 and 4.

**3. What did Ferdinand Lindeman prove in 1882?**
**(a)** It is impossible to find the square of a semicircle. **(b)** That the square root of the hypotenuse of a right triangle can not be found. **(c)** It is possible to find the square of a circle. **(d)** That the square of a circle can not be found with a compass and a straight-edge.

**4. Which was true of Euclid's number theory?**
**(a)** It was incorrect, as proved by Plato. **(b)** It has been proven too basic to be useful. **(c)** It was proven to the true by Hippocrates. **(d)** It has an impact on modern math.

**5. In Elements, how many postulates must be accepted as given?**
**(a)** Eighteen. **(b)** Five. **(c)** Twenty-two. **(d)** Twelve,

**6. What was the same about Apollonius and Erosthanes?**
**(a)** They were both born in the same year. **(b)** They both studied the Universe. **(c)** They both calculated the circumference of the earth. **(d)** They were both mathematicians.

**7. Who was Neil's Abel?**
**(a)** He proved that to solve a quartic equation, one must use more than algebra. **(b)** He demonstrated that Cardano's solution to the cubic was incorrect, **(c)** He proved that quintic equations cannot be solved using algebra. **(d)** He demonstrated the modern version of the Pythagorean Theorem.

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

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

**10. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?**
**(a)** Discrete numbers. **(b)** Perfect numbers. **(c)** Composite numbers. **(d)** Even numbers.

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

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

**13. 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 radius 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 hypotenuse 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 diameter and the other leg equal to the circle's circumference.

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

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

## Short Answer Questions

**1.** According to Euclid, when is a triangle a right triangle?

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

**3.** Which of the following was one of Euclid's great theorems?

**4.** What did Euclid state about pi in Elements?

**5.** How many definitions were stated in Elements?

This section contains 727 words(approx. 3 pages at 300 words per page) |