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

2. What was known about pi, during Archimedes' time?
(a) That is was the relationship between the diameter and circumference of a circle.
(b) That it could not be assigned a relationship between measurements in a circle.
(c) Nothing, the concept of pi was unknown.
(d) That it was never the same number value for a given circle.

3. What was Hippocrates's great advance to mathematics?
(a) He showed how to simplify the area of a triangle.
(b) He showed how to square a figure with curved sides.
(c) He showed how to square a circle.
(d) He showed how to find the angles in a right triangle.

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

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

Short Answer Questions

1. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?

2. Besides being a mathematician, what else other work was Archimedes famous for?

3. How did Archimedes arrive at a number value for pi?

4. As described by Archimedes, what is always true about he diameter of the circle?

5. What does the Pythagorean Theorem state?

(see the answer key)

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