Journey Through Genius: The Great Theorems of Mathematics Quiz | Four Week Quiz A

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

2. Which of the following is true about pi, as described by Dunham.
(a) The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics.
(b) The measurement of pi should not have been so difficult for Archimedes to demonstrate.
(c) The measurement of pi is a challenge that continues into modern mathematics.
(d) The measurement of pi was redetermined after Archimedes's death.

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

4. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to connect any two points with a line and make a circle.
(b) It is possible to draw a circle that contains no lines.
(c) It is possible to draw an arc with any three points.
(d) It is possible to draw a straight line between an infinite number of points.

5. That properties of specific shapes were early Egyptians aware of?
(a) Pi and the diameter of a circle.
(b) Parallelograms.
(c) Irregular solids.
(d) Right triangles.

Short Answer Questions

1. Which of the following was NOT one of the basic definitions in Elements?

2. How many sides did the pentadecagon have, as presented by Euclid?

3. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

4. Which of Euclid's postulates troubled many of the following generations of mathematicians?

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

(see the answer key)

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