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

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

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

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

5. Who asked Tartaglia for his solution to cubic equations?
(a) Fior,
(b) Cardano.
(c) Pacioli.
(d) Fontana.

6. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Pythagoras.
(b) Thales.
(c) Hippocrates.
(d) Aristotle.

7. In Elements, how many postulates must be accepted as given?
(a) Eighteen.
(b) Twenty-two.
(c) Five.
(d) Twelve,

8. Heron devised which of the following methods?
(a) A way to apply mathematics to public health.
(b) A way to solve binomial equations.
(c) A way to determine the volume in a sphere.
(d) A way to determine the area of a triangle.

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

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

11. Who challenged Tartaglia to a contest to solve cubic equations?
(a) Cardano.
(b) Pacioli.
(c) Fior.
(d) del Ferro.

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

13. What was Hippocrates famous for?
(a) His proof on right triangles.
(b) His theorem on the quadrature of the lune.
(c) His proof defining gravity.
(d) His ability to construct circles without a compass.

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

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

Short Answer Questions

1. What does the Pythagorean Theorem state?

2. Which mathematician was first to take the challenge to solve cubic equations?

3. Which of the following can not be solved using algebra?

4. What did Heron's advances put into historical perspective for Dunham?

5. What did Dunham discuss for many pages in this chapter?

(see the answer keys)

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