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

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

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

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

5. How did Lindeman prove his conclusion?
(a) Lindeman proved that all numbers are constructable with a compass and ruler.
(b) Lindeman proved that some numbers are constructable without the use of a compass.
(c) Lindeman proved that square roots are irrational numbers.
(d) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.

6. What did Dunham consider extraordinary about the Elements?
(a) The content was not based on previous authors' work.
(b) How Hippocrates ordered the book.
(c) The content was totally unique.
(d) How geometric proofs were presented.

7. Which of the following can not be solved using algebra?
(a) Triangulation.
(b) Geometric equation.
(c) Quadratic equation.
(d) Quintic equation.

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

9. Which of the following best describes Archimedes as discussed by Dunham?
(a) Loud and arrogant.
(b) Mild-mannered researcher.
(c) Creative but stubborn.
(d) Absent-minded genius.

10. Who acted as the gate keepers of knowledge?
(a) Greek tradesman.
(b) Greek philosophers.
(c) Roman emporers.
(d) Arabian scholars.

11. What was the title of Cardano's book which contained the solution to the cubic?
(a) Elements.
(b) La Magnifica.
(c) Tarsisia.
(d) Ars Magna.

12. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?
(a) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.
(b) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter.
(c) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.
(d) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.

13. What provided most of the content in the book Elements?
(a) Notions.
(b) Hypotheses.
(c) Postulates.
(d) Propositions.

14. Which of the following was one of Euclid's great theorems?
(a) There exists an finite number of prime numbers.
(b) Prime numbers are more comples than discrete numbers.
(c) There exists only infinite and whole numbers.
(d) There exists an infinite number of prime numbers.

15. 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.

Short Answer Questions

1. Which of the following was true about Cardano, according to Dunham?

2. Which is a geometric concept that humans have been aware of since the dawn of agriculture?

3. When was the work of these early thinkers rediscovered again in history?

4. In Elements, how many postulates must be accepted as given?

5. Who challenged Tartaglia to a contest to solve cubic equations?

(see the answer keys)

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