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. 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 circumference.
(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 diameter.
(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.

2. Heron's work referred to the work of what other famous scholar?
(a) Euclid.
(b) Archimedes.
(c) Thales.
(d) Hippocrates.

3. Which of the following is false about the modern implications of Euclid's number theory?
(a) Euclid's recipe for constructing even perfect numbers is incorrect.
(b) Whether there are no odd perfect numbers is still not known.
(c) Euclid gave a good idea for how to construct even perfect numbers.
(d) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.

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

5. Which of the following best describes Archimedes as discussed by Dunham?
(a) Creative but stubborn.
(b) Loud and arrogant.
(c) Mild-mannered researcher.
(d) Absent-minded genius.

Short Answer Questions

1. Which is a geometric concept that humans have been aware of since the dawn of agriculture?

2. Which of the following was NOT one of the basic definitions in Elements?

3. What was the same about Apollonius and Erosthanes?

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

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

(see the answer key)

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