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

Multiple Choice Questions

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

2. That properties of specific shapes were early Egyptians aware of?
(a) Pi and the diameter of a circle.
(b) Parallelograms.
(c) Irregular solids.
(d) Right triangles.

3. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Thales.
(b) Aristotle.
(c) Hippocrates.
(d) Pythagoras.

4. 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 parallel lines.
(d) Euclid's postulate on creating an arc.

5. Who was the author of the book Elements?
(a) Euclid.
(b) Einstein.
(c) Lindemann.
(d) Hippocrates.

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

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

8. Which mathematician was first to take the challenge to solve cubic equations?
(a) Tartaglia.
(b) Luca Pacioli.
(c) Scipione del Ferro.
(d) Niccolo Fontana.

9. What allowed Cardano to justify publishing his book?
(a) He found del Ferro's orgininal solution to the cubic.
(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 was punished as a heretic,

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

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

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

13. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?
(a) Even number.
(b) Nominal number.
(c) Perfect number.
(d) Composite number.

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

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

Short Answer Questions

1. What instruments did the Greeks use to square a shape?

2. What range of values did Archimedes determine for pi?

3. Which shapes as described by Euclid, inspired the Greek philosopher Plato?

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

5. Which of the following was NOT one of the basic definitions in Elements?

(see the answer keys)

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