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

Multiple Choice Questions

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

2. 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 hypotenuse and the other leg equal to the circle's circumference.
(b) 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.
(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 diameter and the other leg equal to the circle's circumference.

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

4. Heron devised which of the following methods?
(a) A way to apply mathematics to public health.
(b) A way to solve binomial equations.
(c) A way to determine the area of a triangle.
(d) A way to determine the volume in a sphere.

5. Which of the following was true about Cardano, according to Dunham?
(a) He had three wives.
(b) He was jailed for heresy.
(c) He was not a mathematician.
(d) He was a priest.

6. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's never proportional to its circumference.
(b) It's equal to the square of the radius.
(c) It's always proportional to its circumference.
(d) It's equal to pi.

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

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

9. When was the work of these early thinkers rediscovered again in history?
(a) In the Renaissance.
(b) In the Elizabethian age.
(c) In the 18th century.
(d) In the 20th century.

10. Which of the following was an important proposition given by Euclid's number theory?
(a) Any perfect number is divisible by some composite number.
(b) Numbers from one to ten are only divisible by composite numbers.
(c) Any even number is divisible by 3.
(d) Any composite number is divisible by some prime number.

11. In general, what did Euclid's number theory describe?
(a) The nature of whole numbers.
(b) The relationship of decimals to integers.
(c) The nature of measuring geometry.
(d) The relationship of fractions to decimals.

12. How do we know about Hippocrates proofs and theorems?
(a) His books and publications.
(b) Mathematicians rewrote all of his proofs after his death,
(c) What is known from archived documents of his time.
(d) What we know is from references of later mathematicians.

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

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

15. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?
(a) Fontana's method.
(b) del Ferro's method.
(c) Pacioli's method.
(d) Cardano's method.

Short Answer Questions

1. Which of Euclid's postulates troubled many of the following generations of mathematicians?

2. In what time period did mathematicians find a solution to cubic equations?

3. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

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

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

(see the answer keys)

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