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

Multiple Choice Questions

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

2. According to Dunham, who was most able to collect knowledge from around the globe?
(a) Greek philosophers.
(b) Greek tradesman.
(c) Arabian scholars.
(d) Roman emporers.

3. Why did Cardano take an oath to secrecy?
(a) It was to the only way to win the contest with Fior,
(b) It was the only way to get his book published.
(c) It was the only way he could become a priest,
(d) It was the only way to get Tartaglia's solution to cubic equations.

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

5. How many sides did the pentadecagon have, as presented by Euclid?
(a) Ten.
(b) Twenty.
(c) Five.
(d) Fifteen.

6. What did Plato use his inspiration from Euclid for?
(a) To create a new theorem of algebra.
(b) To prove Euclid's number theory was incorrect.
(c) To construct his theory on the shape of the Universe.
(d) To classify geometric shapes by their complexity.

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

8. What was true about Heron's theorem as described by Dunham?
(a) It was to determine the volume of a sphere without measuring the circumference.
(b) It was to find the area of a triangle when only the length of the sides are known.
(c) It was to solve equations were only two varibles are known.
(d) It was to determine the area of a circle by measuring a right triangle inside the circle.

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

11. Besides being a mathematician, what else other work was Archimedes famous for?
(a) Politician.
(b) Inventor and scientist.
(c) Artist and musician.
(d) Doctor and writer,

12. Where was Archimedes born?
(a) Olympia.
(b) Rome.
(c) Sicily.
(d) Athens.

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

14. What instruments did the Greeks use to square a shape?
(a) A pendulum.
(b) A compass and a ruled straight-edge.
(c) A sphere and ruler.
(d) A small grid.

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

Short Answer Questions

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

2. After Hippocrates, what shape did the Greeks attempt to square without success?

3. What did Ferdinand Lindeman prove in 1882?

4. Which of the following becomes an important definition in mathematics that was first presented in Elements?

5. What do we know in modern times about Heron?

(see the answer keys)

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