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. Which of Euclid's postulates troubled many of the following generations of mathematicians?
(a) Euclid's postulate on right triangles.
(b) Euclid's postulate on creating an arc.
(c) Euclid's proof on right triangles.
(d) Euclid's postulate on parallel lines.

2. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?
(a) Quadrature.
(b) Cubation.
(c) Square root.
(d) Triangulation.

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

4. What did Hippocrates do that advanced mathematical methods?
(a) He built theorems based on sequencially more complex proofs.
(b) He created a new ways to disprove theories.
(c) He proved that mathematics can be applied in a unlogical order.
(d) He demonstrated that geometry does not have to be based on previous knowledge.

5. What did Gauss set out to prove?
(a) That the sum of the angles in a triangle is 180 degrees.
(b) That a right angle is always equal to 90 degrees.
(c) That Euclid's postulate on straight lines was incorrect.
(d) That a circle can have less than 360 degrees.

6. Where was Neil's Abel from?
(a) Norway.
(b) Ireland.
(c) Great Britian,
(d) Finland.

7. Who was Eratosthanes?
(a) He was the first to study political sciences.
(b) He was a mathematician, and leading doctor.
(c) He was the chief librarian, and a mathematician.
(d) He was a teacher and philosopher.

8. Which mathematician was first to take the challenge to solve cubic equations?
(a) Tartaglia.
(b) Scipione del Ferro.
(c) Luca Pacioli.
(d) Niccolo Fontana.

9. Which of the following becomes an important definition in mathematics that was first presented in Elements?
(a) Parallel line.
(b) Intersection.
(c) 180 degree angle.
(d) Circle.

10. What did Euclid do in his 48th proposition?
(a) Euclid proved the Pythagorean Theorem.
(b) Euclid demonstrated the faults of the Pythagorean Theorem.
(c) Euclid demonstrated how to use the Pythagorean Theorem.
(d) Euclid proved the converse of the Pythagorean Theorem.

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

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

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

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

15. Which was true of Euclid's number theory?
(a) It was incorrect, as proved by Plato.
(b) It was proven to the true by Hippocrates.
(c) It has been proven too basic to be useful.
(d) It has an impact on modern math.

Short Answer Questions

1. What was true about Heron's theorem as described by Dunham?

2. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

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

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

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

(see the answer keys)

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