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. Where was the modern number system developed?
(a) In the East.
(b) In the West.
(c) In ancient Rome.
(d) In ancient Alexanderia.

2. Which of the following were an example of twin primes?
(a) 19 and 22.
(b) 11 and 13.
(c) 2 and 6.
(d) 15 and 16.

3. What did Heron's advances put into historical perspective for Dunham?
(a) A change in political theory across the globe.
(b) A shift in information flow that ignored socioeconomic order.
(c) A shift in learning across continents.
(d) A change in learning foundations in the ancient scholarly universities.

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

5. Which is a geometric concept that humans have been aware of since the dawn of agriculture?
(a) Metric system.
(b) Volume.
(c) Area.
(d) Gravity.

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

7. Exactly what limit is reached at a quartic equation?
(a) The limit of the Pythagorean Theorem.
(b) The limit of the decompressed cubic method.
(c) The limit of logical geometric proofs.
(d) The limit of algebra.

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

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

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

11. What was true about Heron's theorem as described by Dunham?
(a) It was to find the area of a triangle when only the length of the sides are known.
(b) It was to solve equations were only two varibles are known.
(c) It was to determine the area of a circle by measuring a right triangle inside the circle.
(d) It was to determine the volume of a sphere without measuring the circumference.

12. In what time period did mathematicians find a solution to cubic equations?
(a) Seventeeth century.
(b) Thirteenth century.
(c) Twentieth century.
(d) Fifteen century.

13. When was the work of these early thinkers rediscovered again in history?
(a) In the Renaissance.
(b) In the 18th century.
(c) In the 20th century.
(d) In the Elizabethian age.

14. Which of the following was NOT one of the basic definitions in Elements?
(a) Straight Line.
(b) Right angles.
(c) Parabola.
(d) Line.

15. Which of the following best describes Cardano's character?
(a) Flirtacious.
(b) Eccentric.
(c) Religious.
(d) Arrogant.

Short Answer Questions

1. What did Euclid state about pi in Elements?

2. What was Eratosthanes most famous for?

3. What did Dunham consider extraordinary about the Elements?

4. What does the Pythagorean Theorem state?

5. What range of values did Archimedes determine for pi?

(see the answer keys)

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