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

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

3. What allowed Cardano to justify publishing his book?
(a) He found Fior's documents which spoke against Tartaglia.
(b) He was dead, and the book was really published by his student.
(c) He found del Ferro's orgininal solution to the cubic.
(d) He was punished as a heretic,

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

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

6. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the relationship of sine to cosine.
(b) He studied the relationship between ratios in triangles.
(c) He studied the volume and surface area of spheres, cones, and cylinders.
(d) He studied the volume to surface area ratios of cubes.

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

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

9. What did most of Heron's work deal with?
(a) Philosophical questions on the origins of the universe.
(b) Practical mathematics applications.
(c) Practical solutions to public problems.
(d) Theoretical mathematics.

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

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

12. What did Ferdinand Lindeman prove in 1882?
(a) It is impossible to find the square of a semicircle.
(b) It is possible to find the square of a circle.
(c) That the square of a circle can not be found with a compass and a straight-edge.
(d) That the square root of the hypotenuse of a right triangle can not be found.

13. What did Euclid state about pi in Elements?
(a) The proportion of diameter to area is never equal.
(b) The proportion of area to circumference is never equal.
(c) There is a constant relationship between the area of a circle and the square of its diameter.
(d) There is no relationship between the area of a circle and its circumference.

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

15. What was Hippocrates's great advance to mathematics?
(a) He showed how to simplify the area of a triangle.
(b) He showed how to square a circle.
(c) He showed how to square a figure with curved sides.
(d) He showed how to find the angles in a right triangle.

Short Answer Questions

1. What was true about Hippocrates's proof?

2. Which of the following could NOT be included as a step in Euclid's great theorem?

3. What was known about pi, during Archimedes' time?

4. What was Hippocrates famous for?

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

(see the answer keys)

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