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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 instruments did the Greeks use to square a shape?**
**(a)** A sphere and ruler. **(b)** A pendulum. **(c)** A compass and a ruled straight-edge. **(d)** A small grid.

**2. What did Plato use his inspiration from Euclid for?**
**(a)** To construct his theory on the shape of the Universe. **(b)** To classify geometric shapes by their complexity. **(c)** To create a new theorem of algebra. **(d)** To prove Euclid's number theory was incorrect.

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

**4. After Hippocrates, what shape did the Greeks attempt to square without success?**
**(a)** Circle. **(b)** Pentagon. **(c)** Parallelogram. **(d)** Hemisphere.

**5. What range of values did Archimedes determine for pi?**
**(a)** Between 3 and 3 1/2. **(b)** Between 3 and 4. **(c)** Between 3 10/11 and 3 1/7. **(d)** Between 3 1/2 and 3 5/8.

## Short Answer Questions

**1.** Which is one of the common notions presented in Elements?

**2.** In what century did Archimedes live?

**3.** How do we know about Hippocrates proofs and theorems?

**4.** What does the Pythagorean Theorem state?

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

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