Journey Through Genius: The Great Theorems of Mathematics Quiz | Two Week Quiz A

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through A Gem from Isaac Newton.

Multiple Choice Questions

1. What did Archimedes manage to prove using Euclid's ideas?
(a) That the square of a diameter is equal to pi.
(b) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
(c) That the value of pi is proportional to the area of the circle.
(d) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.

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

3. Which words best describe how solid proofs were developed in Elements?
(a) Simple arguments.
(b) Programmed order.
(c) Axiomatic framework.
(d) Inverted scaffold.

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

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

Short Answer Questions

1. To how many decimal places did Newton determine the number for pi?

2. What is true about prime numbers?

3. Who wrote a treatise that supposed that cubic equations may be impossible to solve?

4. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

5. Exactly what limit is reached at a quartic equation?

(see the answer key)

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