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

Multiple Choice Questions

1. What did Dunham discuss for many pages in this chapter?
(a) Heron's origins of the universe.
(b) Heron's political tendancy.
(c) Heron's religious beliefs-
(d) Heron's complicated proof.

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

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

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

5. What did Dunham consider extraordinary about the Elements?
(a) The content was totally unique.
(b) How Hippocrates ordered the book.
(c) How geometric proofs were presented.
(d) The content was not based on previous authors' work.

6. Which of the following were an example of twin primes?
(a) 15 and 16.
(b) 19 and 22.
(c) 11 and 13.
(d) 2 and 6.

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

8. What was Hippocrates's great advance to mathematics?
(a) He showed how to square a circle.
(b) He showed how to simplify the area of a triangle.
(c) He showed how to square a figure with curved sides.
(d) He showed how to find the angles in a right triangle.

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

10. Who acted as the gate keepers of knowledge?
(a) Arabian scholars.
(b) Greek philosophers.
(c) Greek tradesman.
(d) Roman emporers.

11. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to draw a circle that contains no lines.
(b) It is possible to draw a straight line between an infinite number of points.
(c) It is possible to connect any two points with a line and make a circle.
(d) It is possible to draw an arc with any three points.

12. Who was del Ferro's student?
(a) Gerolamo Cardano.
(b) Luca Pacioli.
(c) Antonio Fior.
(d) Niccolo Fontana.

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

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

15. What did Gauss set out to prove?
(a) That a circle can have less than 360 degrees.
(b) That a right angle is always equal to 90 degrees.
(c) That Euclid's postulate on straight lines was incorrect.
(d) That the sum of the angles in a triangle is 180 degrees.

Short Answer Questions

1. Which of the following was NOT one of Gauss' discoveries?

2. Where did Hippocrates come from?

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

4. What did Dunham consider as Archimedes's "masterpiece"?

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

(see the answer keys)

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