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

Multiple Choice Questions

1. Which of the following can not be solved using algebra?
(a) Geometric equation.
(b) Triangulation.
(c) Quadratic equation.
(d) Quintic equation.

2. Which of the following becomes an important definition in mathematics that was first presented in Elements?
(a) Intersection.
(b) Circle.
(c) 180 degree angle.
(d) Parallel line.

3. Which of the following is true about pi, as described by Dunham.
(a) The measurement of pi was redetermined after Archimedes's death.
(b) The measurement of pi should not have been so difficult for Archimedes to demonstrate.
(c) The measurement of pi is a challenge that continues into modern mathematics.
(d) The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics.

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

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

6. Which of the following was NOT true about Archimedes, according to Dunham?
(a) He died during the fall of Syracuse.
(b) Archimedes died because he refused to follow orders until he completed a math problem.
(c) His death was described as being by the hands of a Roman invader.
(d) He died as a soldier.

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

8. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's never proportional to its circumference.
(b) It's always proportional to its circumference.
(c) It's equal to the square of the radius.
(d) It's equal to pi.

9. What was Eratosthanes most famous for?
(a) He showed that there are no even prime numbers.
(b) He developed a simple way to find prime numbers and for determining the circumference of the Earth.
(c) He showed that the Earth must be a sphere.
(d) He developed a way to navigate using logitude and latitude.

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

11. Which of the following best describes Archimedes as discussed by Dunham?
(a) Loud and arrogant.
(b) Absent-minded genius.
(c) Creative but stubborn.
(d) Mild-mannered researcher.

12. Where was Neil's Abel from?
(a) Norway.
(b) Finland.
(c) Great Britian,
(d) Ireland.

13. 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) Whether there are no odd perfect numbers is still not known.
(c) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.
(d) Euclid's recipe for constructing even perfect numbers is incorrect.

14. What did Gauss set out to prove?
(a) That Euclid's postulate on straight lines was incorrect.
(b) That a right angle is always equal to 90 degrees.
(c) That a circle can have less than 360 degrees.
(d) That the sum of the angles in a triangle is 180 degrees.

15. What did Apollonius work with in mathematics?
(a) He worked on advanced algebra.
(b) He develped a way to measure the volume of a sphere.
(c) He discovered the algrebraic equation.
(d) He worked on conics.

Short Answer Questions

1. How did Archimedes demonstrate his theory of pi?

2. What allowed Cardano to justify publishing his book?

3. What was true about Hippocrates's proof?

4. Which of Euclid's postulates troubled many of the following generations of mathematicians?

5. Which of the following is true in modern math about twin primes?

(see the answer keys)

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