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This quiz consists of 5 multiple choice and 5 short answer questions through Euclid's Proof of the Pythagorean Theorem.

## Multiple Choice Questions

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

**2. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?**
**(a)** Parallel lines. **(b)** Intersection. **(c)** Circle. **(d)** 180 degree angle.

**3. How do we know about Hippocrates proofs and theorems?**
**(a)** What we know is from references of later mathematicians. **(b)** What is known from archived documents of his time. **(c)** Mathematicians rewrote all of his proofs after his death, **(d)** His books and publications.

**4. Which of the following was NOT one of Gauss' discoveries?**
**(a)** That angles in a triangles can not add up to more than 180 degrees. **(b)** "Non-euclidean" geometry. **(c)** That under Euclid's definition parallel lines can intersect. **(d)** That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.

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

## Short Answer Questions

**1.** What did Ferdinand Lindeman prove in 1882?

**2.** How many definitions were stated in Elements?

**3.** How did Lindeman prove his conclusion?

**4.** What did Gauss set out to prove?

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

This section contains 380 words(approx. 2 pages at 300 words per page) |