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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 did the Pythagorean Theorem accomplish for mathematics?**
**(a)** The concept of providing a logical proof. **(b)** The ability to find square roots. **(c)** The ability to measure angles. **(d)** The concept of constructing useful mathematics.

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

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

**4. What did Ferdinand Lindeman prove in 1882?**
**(a)** It is impossible to find the square of a semicircle. **(b)** That the square of a circle can not be found with a compass and a straight-edge. **(c)** That the square root of the hypotenuse of a right triangle can not be found. **(d)** It is possible to find the square of a circle.

**5. What was most useful about finding the square of a shape, before Hippocrates?**
**(a)** It was useful in finding the area of circles. **(b)** It was useful in determining the distance between two points. **(c)** It was useful in creating simple elevation maps, **(d)** It was useful in finding the area of oddly shaped pieces of land.

## Short Answer Questions

**1.** What did Hippocrates do that advanced mathematical methods?

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

**3.** How did Archimedes demonstrate his theory of pi?

**4.** Where was Archimedes born?

**5.** Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

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