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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 was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?
(a) Euclid constructed squares on the sides of right triangles.
(b) Euclid used propositions about similar angles and parallel lines.
(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.

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

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

4. How did Lindeman prove his conclusion?
(a) Lindeman proved that square roots are irrational numbers.
(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 some numbers are constructable without the use of a compass.

5. What did most of Heron's work deal with?
(a) Practical solutions to public problems.
(b) Practical mathematics applications.
(c) Theoretical mathematics.
(d) Philosophical questions on the origins of the universe.

6. What did Hippocrates do that advanced mathematical methods?
(a) He demonstrated that geometry does not have to be based on previous knowledge.
(b) He created a new ways to disprove theories.
(c) He built theorems based on sequencially more complex proofs.
(d) He proved that mathematics can be applied in a unlogical order.

7. What did Euclid state about pi in Elements?
(a) There is no relationship between the area of a circle and its circumference.
(b) The proportion of area to circumference is never equal.
(c) The proportion of diameter to area is never equal.
(d) There is a constant relationship between the area of a circle and the square of its diameter.

8. In what century did Archimedes live?
(a) Nineteeth century A.D.
(b) Twelthf century A.D.
(c) First century A.D,
(d) Third century B.C.

9. What is true about prime numbers?
(a) Prime numbers can never be an odd number.
(b) Prime numbers can not exist in a finite series.
(c) That for every group of prime numbers, there exists at least one more prime.
(d) Prime numbers are not divisible by other numbers.

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

11. 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 relationship between ratios in triangles.
(c) He studied the volume to surface area ratios of cubes.
(d) He studied the relationship of sine to cosine.

12. What was most useful about finding the square of a shape, before Hippocrates?
(a) It was useful in finding the area of oddly shaped pieces of land.
(b) It was useful in determining the distance between two points.
(c) It was useful in finding the area of circles.
(d) It was useful in creating simple elevation maps,

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

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

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

Short Answer Questions

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

2. According to Dunham, who was most able to collect knowledge from around the globe?

3. Dunham showed that Heron's proof could also be used as which of the following?

4. In Elements, how many postulates must be accepted as given?

5. Where was the modern number system developed?

(see the answer keys)

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