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 the following was NOT true about Archimedes, according to Dunham?
(a) Archimedes died because he refused to follow orders until he completed a math problem.
(b) He died during the fall of Syracuse.
(c) He died as a soldier.
(d) His death was described as being by the hands of a Roman invader.

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

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

4. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's equal to pi.
(b) It's always proportional to its circumference.
(c) It's equal to the square of the radius.
(d) It's never proportional to its circumference.

5. What do we know in modern times about Heron?
(a) We know he lived in Rome.
(b) We know very little, but much of his work survives.
(c) We know he was an influencial scholar, but we don't know who his students were.
(d) We know he was a teacher and philosopher but much of his work has been lost.

6. What was true about Hippocrates's proof?
(a) The proof was exceedingly difficult and not understood at the time.
(b) It was fairly easy and simple.
(c) It was useful for circles.
(d) The proof was easy if their was advanced technology available.

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

8. 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.

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

10. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?
(a) Fontana's method.
(b) Cardano's method.
(c) Pacioli's method.
(d) del Ferro's method.

11. Who was Heron?
(a) A philosopher from Greece.
(b) A matematician from Alexanderia.
(c) A physician from the far East.
(d) A politician from Rome.

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

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

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

15. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to draw an arc with any three points.
(b) It is possible to draw a circle that contains no lines.
(c) It is possible to connect any two points with a line and make a circle.
(d) It is possible to draw a straight line between an infinite number of points.

Short Answer Questions

1. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?

2. Who was Neil's Abel?

3. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

4. Which of the following was NOT one of Gauss' discoveries?

5. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

(see the answer keys)

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