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This quiz consists of 5 multiple choice and 5 short answer questions through Cantor and the Transfinite Realm.

Multiple Choice Questions

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

2. According to Euclid, when is a triangle a right triangle?
(a) When a triangle does not have a side which can be considered a hypotenuse.
(b) When a triangle can be constructed with three unequal sides.
(c) When a triangle has three sides whose squares are equal to the area of the triangle.
(d) When a triangle has a side whose square is the sum of the squares of the two legs.

3. Where did George Cantor live in the 1860s and 1870s?
(a) Russia.
(b) Britian.
(c) Germany.
(d) Scotland.

4. According to Dunham, who was most able to collect knowledge from around the globe?
(a) Roman emporers.
(b) Arabian scholars.
(c) Greek tradesman.
(d) Greek philosophers.

5. What did Cantor develop?
(a) A method to factor very large composite numbers.
(b) A method to find the sum of a geometric series.
(c) A system to identify prime numbers of very large size.
(d) A system to compare relative sizes of cardinal numbers.

Short Answer Questions

1. What did Dunham claim about Archimedes's determination of a number value for pi?

2. How many definitions were stated in Elements?

3. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

4. What did Euler's sum surprisingly connect?

5. What provided most of the content in the book Elements?

(see the answer key)

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