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This quiz consists of 5 multiple choice and 5 short answer questions through A Sampler of Euler's Number Theory.

Multiple Choice Questions

1. Which of the following was an important proposition given by Euclid's number theory?
(a) Numbers from one to ten are only divisible by composite numbers.
(b) Any composite number is divisible by some prime number.
(c) Any even number is divisible by 3.
(d) Any perfect number is divisible by some composite number.

2. What did Dunham discuss for many pages in this chapter?
(a) Heron's complicated proof.
(b) Heron's origins of the universe.
(c) Heron's religious beliefs-
(d) Heron's political tendancy.

3. Which of the following was NOT one of Gauss' discoveries?
(a) That under Euclid's definition parallel lines can intersect.
(b) That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.
(c) "Non-euclidean" geometry.
(d) That angles in a triangles can not add up to more than 180 degrees.

4. What did Dunham consider as Archimedes's "masterpiece"?
(a) Archimedes' work on shperes, cones, and cylinders.
(b) Archimedes' work on volume to surface area ratios.
(c) Archimedes' work on determining a number value for pi.
(d) Archimedes' work on determining angular measurements.

5. Who else, besides Newton, independently discovered a calculus method?
(a) Isaac Barrow.
(b) John Napier.
(c) Pierre de Fermat.
(d) Gottfried Leibniz.

Short Answer Questions

1. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?

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

3. Who was Heron?

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

5. Which words best describe how solid proofs were developed in Elements?

(see the answer key)

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