Journey Through Genius: The Great Theorems of Mathematics Quiz | Four Week Quiz B

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through A Sampler of Euler's Number Theory.

Multiple Choice Questions

1. Where did Newton go to school before he went to Cambridge?
(a) Cambridge Prep.
(b) Charles II Grammar School.
(c) The King's School.
(d) Oxford Grammar School.

2. Which of the following demonstrates the successive squared denominator series?
(a) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(b) 1 + 1/4 + 1/9 + 1/16 . . .
(c) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(d) 1 + 1/2 + 3/4 + 4/5 . . .

3. Dunham showed that Heron's proof could also be used as which of the following?
(a) A proof of Archimedes' number theory.
(b) A proof of Euclid's number theory
(c) A proof of the Pythagorean Theorem.
(d) A proof of Hippocrates' squared areas.

4. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Even numbers.
(b) Perfect numbers.
(c) Composite numbers.
(d) Discrete numbers.

5. 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 diameter 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 radius and the other leg equal to the circle's circumference.

Short Answer Questions

1. In what area was Gauss especially interested?

2. What did Euler prove about 2²ⁿ + 1?

3. Where was Archimedes born?

4. What is true about prime numbers?

5. What is one proof that Euler was able to prove?

(see the answer key)

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