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

Multiple Choice Questions

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

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

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

4. What was known about pi, during Archimedes' time?
(a) That it could not be assigned a relationship between measurements in a circle.
(b) That it was never the same number value for a given circle.
(c) That is was the relationship between the diameter and circumference of a circle.
(d) Nothing, the concept of pi was unknown.

5. What did Euclid do in his 48th proposition?
(a) Euclid proved the Pythagorean Theorem.
(b) Euclid proved the converse of the Pythagorean Theorem.
(c) Euclid demonstrated how to use the Pythagorean Theorem.
(d) Euclid demonstrated the faults of the Pythagorean Theorem.

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

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

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

9. What was the title of Cardano's book which contained the solution to the cubic?
(a) Elements.
(b) Ars Magna.
(c) Tarsisia.
(d) La Magnifica.

10. Dunham showed that Heron's proof could also be used as which of the following?
(a) A proof of Euclid's number theory
(b) A proof of Hippocrates' squared areas.
(c) A proof of Archimedes' number theory.
(d) A proof of the Pythagorean Theorem.

11. Who was Eratosthanes?
(a) He was a mathematician, and leading doctor.
(b) He was the chief librarian, and a mathematician.
(c) He was a teacher and philosopher.
(d) He was the first to study political sciences.

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

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

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

15. Which of the following could NOT be included as a step in Euclid's great theorem?
(a) If a new number is found to be composite, then it must have some prime as a divisor.
(b) Take a finite group of primes and add them together, plus one.
(c) Divide a infinite group of primes by the sum of their composites.
(d) After summation, the new number can be prime or composite.

Short Answer Questions

1. How many sides did the pentadecagon have, as presented by Euclid?

2. What did Dunham consider extraordinary about the Elements?

3. In general, what did Euclid's number theory describe?

4. What was Hippocrates's great advance to mathematics?

5. Why did Cardano take an oath to secrecy?

(see the answer keys)

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