Journey Through Genius: The Great Theorems of Mathematics Quiz | Eight Week Quiz C

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

Multiple Choice Questions

1. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?
(a) Euclid used his own axioms and propositions to show relationships,
(b) Euclid used propositions about similar angles and parallel lines.
(c) Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs.
(d) Euclid constructed squares on the sides of right triangles.

2. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on right triangles.
(b) Euclid's postulate on parallel lines.
(c) Euclid's proof on right triangles.
(d) Euclid's postulate on creating an arc.

3. Which of the following is true in modern math about twin primes?
(a) We don't know if they are finite or infinite.
(b) They are infinite.
(c) Their sum is always another prime number.
(d) They are not considered whole numbers.

4. What range of values did Archimedes determine for pi?
(a) Between 3 10/11 and 3 1/7.
(b) Between 3 and 3 1/2.
(c) Between 3 1/2 and 3 5/8.
(d) Between 3 and 4.

5. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Pythagoras.
(b) Hippocrates.
(c) Thales.
(d) Aristotle.

Short Answer Questions

1. What did Heron's advances put into historical perspective for Dunham?

2. How did Archimedes demonstrate his theory of pi?

3. Heron's work referred to the work of what other famous scholar?

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

5. What was known about pi, during Archimedes' time?

(see the answer key)

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