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This quiz consists of 5 multiple choice and 5 short answer questions through Archimedes' Determination of Circular Area.

Multiple Choice Questions

1. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?
(a) Square root.
(b) Triangulation.
(c) Cubation.
(d) Quadrature.

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

3. Which words best describe how solid proofs were developed in Elements?
(a) Inverted scaffold.
(b) Axiomatic framework.
(c) Simple arguments.
(d) Programmed order.

4. What was the bases of Hippocrates's proof ?
(a) Properties of squares and cubes.
(b) Properties of points and lines.
(c) Properties of area to volume measurements.
(d) Properties of triangles and semicircles.

5. How did Lindeman prove his conclusion?
(a) Lindeman proved that all numbers are constructable with a compass and ruler.
(b) Lindeman proved that square roots are irrational numbers.
(c) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(d) Lindeman proved that some numbers are constructable without the use of a compass.

Short Answer Questions

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

2. Which of the following is true about pi, as described by Dunham.

3. Which of the following is false about the modern implications of Euclid's number theory?

4. What is true about prime numbers?

5. What was most useful about finding the square of a shape, before Hippocrates?

(see the answer key)

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