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

William Dunham (mathematician)
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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. What range of values did Archimedes determine for pi?
(a) Between 3 10/11 and 3 1/7.
(b) Between 3 and 4.
(c) Between 3 1/2 and 3 5/8.
(d) Between 3 and 3 1/2.

2. Why did Cardano take an oath to secrecy?
(a) It was the only way to get his book published.
(b) It was the only way to get Tartaglia's solution to cubic equations.
(c) It was to the only way to win the contest with Fior,
(d) It was the only way he could become a priest,

3. Which shapes as described by Euclid, inspired the Greek philosopher Plato?
(a) Manifolds.
(b) Regular polyhedrons.
(c) Triangles.
(d) Spheres and cones.

4. How do we know about Hippocrates proofs and theorems?
(a) His books and publications.
(b) What is known from archived documents of his time.
(c) What we know is from references of later mathematicians.
(d) Mathematicians rewrote all of his proofs after his death,

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

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

7. In Elements, how many postulates must be accepted as given?
(a) Five.
(b) Eighteen.
(c) Twelve,
(d) Twenty-two.

8. What did most of Heron's work deal with?
(a) Practical mathematics applications.
(b) Practical solutions to public problems.
(c) Philosophical questions on the origins of the universe.
(d) Theoretical mathematics.

9. According to Euclid, when is a triangle a right triangle?
(a) When a triangle can be constructed with three unequal sides.
(b) When a triangle has three sides whose squares are equal to the area of the triangle.
(c) When a triangle has a side whose square is the sum of the squares of the two legs.
(d) When a triangle does not have a side which can be considered a hypotenuse.

10. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?
(a) Triangle.
(b) Hexagon.
(c) Hyperbola.
(d) Pentagon.

11. Who challenged Tartaglia to a contest to solve cubic equations?
(a) Fior.
(b) Pacioli.
(c) Cardano.
(d) del Ferro.

12. Who asked Tartaglia for his solution to cubic equations?
(a) Pacioli.
(b) Cardano.
(c) Fontana.
(d) Fior,

13. Where did Hippocrates come from?
(a) Chios.
(b) Athens.
(c) Rome.
(d) Constinople.

14. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number was perfectly correct.
(b) Archimedes's number was very good, considering he did not have a way to calculate square roots.
(c) Archimedes's number was not very accurate, considering the technology of his time.
(d) Archimedes's number could have been better if he had understood Euclid's work better,

15. Which of the following is true about pi, as described by Dunham.
(a) The measurement of pi should not have been so difficult for Archimedes to demonstrate.
(b) The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics.
(c) The measurement of pi is a challenge that continues into modern mathematics.
(d) The measurement of pi was redetermined after Archimedes's death.

Short Answer Questions

1. Which of the following becomes an important definition in mathematics that was first presented in Elements?

2. Heron devised which of the following methods?

3. What did the Pythagorean Theorem accomplish for mathematics?

4. What was Hippocrates famous for?

5. How did Lindeman prove his conclusion?

(see the answer keys)

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