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 were the proofs in Elements based on?
(a) Basic definitions.
(b) Ancient greek geometry.
(c) Lindeman's method.
(d) Novel notions.

2. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) Intersection.
(b) Parallel lines.
(c) 180 degree angle.
(d) Circle.

3. In what century did Archimedes live?
(a) Twelthf century A.D.
(b) First century A.D,
(c) Third century B.C.
(d) Nineteeth century A.D.

4. What else, besides a solution to cubic equations, was in Cardano's book?
(a) A proof of the Pythagorean Theorem.
(b) A solution to quartic equations.
(c) A suggested method to depress all complex geometry.
(d) An alegrabic solution to quintic equations,

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

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

7. What did Apollonius work with in mathematics?
(a) He discovered the algrebraic equation.
(b) He worked on conics.
(c) He worked on advanced algebra.
(d) He develped a way to measure the volume of a sphere.

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

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

10. After Hippocrates, what shape did the Greeks attempt to square without success?
(a) Circle.
(b) Pentagon.
(c) Parallelogram.
(d) Hemisphere.

11. Which of the following was true about Cardano, according to Dunham?
(a) He was not a mathematician.
(b) He was jailed for heresy.
(c) He had three wives.
(d) He was a priest.

12. Which of the following could NOT be included as a step in Euclid's great theorem?
(a) Divide a infinite group of primes by the sum of their composites.
(b) If a new number is found to be composite, then it must have some prime as a divisor.
(c) Take a finite group of primes and add them together, plus one.
(d) After summation, the new number can be prime or composite.

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

14. Which city was the center of thinking and learning in Third century BC?
(a) Rome.
(b) Olympia.
(c) Alexandria.
(d) Athens.

15. In general, what did Euclid's number theory describe?
(a) The relationship of decimals to integers.
(b) The relationship of fractions to decimals.
(c) The nature of whole numbers.
(d) The nature of measuring geometry.

Short Answer Questions

1. Which of the following was one of Euclid's great theorems?

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

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

4. What did Dunham claim about Archimedes's determination of a number value for pi?

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

(see the answer keys)

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