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

Multiple Choice Questions

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

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

3. What did Heron's advances put into historical perspective for Dunham?
(a) A change in learning foundations in the ancient scholarly universities.
(b) A shift in learning across continents.
(c) A change in political theory across the globe.
(d) A shift in information flow that ignored socioeconomic order.

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

5. What was the same about Apollonius and Erosthanes?
(a) They were both mathematicians.
(b) They were both born in the same year.
(c) They both studied the Universe.
(d) They both calculated the circumference of the earth.

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

7. What is a "depressed cubic"?
(a) A method to simpify the x squared value in a cubic equation.
(b) A method to solve equations with two variables.
(c) A method to logically square all the factors in a cubic equation.
(d) A method to simplify measuring complex geometric forms.

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

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

10. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?
(a) Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr².
(b) Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference.
(c) Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference.
(d) The area of a triangle is one half the base times the height.

11. How did Archimedes arrive at a number value for pi?
(a) By constructing successively smaller circles inside circles until he realized all of their ratios of diameter to area were equal.
(b) By proving that pi could not be a negative number.
(c) By constructing multi-sided polygons inside and outside a circle and determining their perimeters.
(d) By proving pi could not be equal to one.

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

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

14. 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.

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

Short Answer Questions

1. Which city was the center of thinking and learning in Third century BC?

2. Which of the following is true about pi, as described by Dunham.

3. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?

4. What did Dunham consider extraordinary about the Elements?

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

(see the answer keys)

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