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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 constructing useful mathematics. **(b)** The concept of providing a logical proof. **(c)** The ability to measure angles. **(d)** The ability to find square roots.

**2. Which of the following was NOT one of the basic definitions in Elements?**
**(a)** Straight Line. **(b)** Line. **(c)** Parabola. **(d)** Right angles.

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

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

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

## Short Answer Questions

**1.** What shape was NOT demonstrated in the Elements as having a relationship to other shapes?

**2.** What was the bases of Hippocrates's proof ?

**3.** Which of the following is false about the modern implications of Euclid's number theory?

**4.** According to Euclid, when is a triangle a right triangle?

**5.** What was Hippocrates famous for?

This section contains 410 words(approx. 2 pages at 300 words per page) |