Journey Through Genius: The Great Theorems of Mathematics Test | Mid-Book Test - Medium

William Dunham (mathematician)
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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. What was Euclid's definition of a prime number?
(a) Numbers which can only be divided by themselves and 1.
(b) Numbers which contain an infinite number of composite numbers.
(c) Numbers which are divisible by 2.
(d) Numbers which do not, and can not, contain a perfect number.

2. Who wrote a treatise that supposed that cubic equations may be impossible to solve?
(a) Niccolo Fontana.
(b) Gerolamo Cardano.
(c) Luca Pacioli.
(d) Scipione del Ferro.

3. What did Plato use his inspiration from Euclid for?
(a) To construct his theory on the shape of the Universe.
(b) To prove Euclid's number theory was incorrect.
(c) To create a new theorem of algebra.
(d) To classify geometric shapes by their complexity.

4. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the volume to surface area ratios of cubes.
(b) He studied the relationship between ratios in triangles.
(c) He studied the volume and surface area of spheres, cones, and cylinders.
(d) He studied the relationship of sine to cosine.

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

Short Answer Questions

1. What did Gauss set out to prove?

2. What was Hippocrates famous for?

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

4. In what century did Archimedes live?

5. Who acted as the gate keepers of knowledge?

Short Essay Questions

1. What was the great theorem of this chapter? Describe it briefly.

2. Who was Luca Pacioli, and what controversy was sparked over his writings?

3. Who was Heron, and what is known about him today?

4. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

5. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

6. Explain how Gottfried Leibniz was able to publish his method of calculus.

7. Summarize, in a sentence, what was Hippocates's great theorem, and what was it based on according to Dunham?

8. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

9. What did Euclid state for his theory on prime numbers?

10. Explain why Eulers sum of π²/6 was in some ways surprising.

(see the answer keys)

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