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

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Cardano and the Solution of the Cubic.

Multiple Choice Questions

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

2. Which is one of the common notions presented in Elements?
(a) "Things which are equal to the same thing are also equal to each other."
(b) "Points with equal values can be connected with a line of equal value."
(c) "Things with are equal have an inverse that is equal."
(d) "The inverse of a line makes a circle."

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

4. 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.

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

Short Answer Questions

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

2. What did Euclid state about pi in Elements?

3. Which of the following was NOT defined by Euclid?

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

5. Which of the following could NOT be included as a step in Euclid's great theorem?

(see the answer key)

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