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. Which of the following was NOT one of Gauss' discoveries?
(a) That angles in a triangles can not add up to more than 180 degrees.
(b) That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.
(c) "Non-euclidean" geometry.
(d) That under Euclid's definition parallel lines can intersect.

2. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?
(a) Nominal number.
(b) Composite number.
(c) Perfect number.
(d) Even number.

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

4. What was most useful about finding the square of a shape, before Hippocrates?
(a) It was useful in creating simple elevation maps,
(b) It was useful in determining the distance between two points.
(c) It was useful in finding the area of oddly shaped pieces of land.
(d) It was useful in finding the area of circles.

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

Short Answer Questions

1. What do we know in modern times about Heron?

2. How do we know about Hippocrates proofs and theorems?

3. Who asked Tartaglia for his solution to cubic equations?

4. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

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

Short Essay Questions

1. How many definitions were in Euclid's book? List some of the definitions he included.

2. Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

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

4. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

5. Explain who was Gerolamo Cardano, and how did he become involved with the solution to the cubic.

6. Describe who was Archimedes and how Dunham described his character.

7. Describe Euclid's postulates and notions in how they were important in constructing his proofs.

8. What was Euclid's definition of composite and perfect numbers?

9. Describe how Cardano eventually publishes the solution to cubic equations.

10. Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

(see the answer keys)

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