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This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

## Multiple Choice Questions

**1. In Elements, how many postulates must be accepted as given?**
**(a)** Twelve, **(b)** Twenty-two. **(c)** Eighteen. **(d)** Five.

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

**3. Which of the following is an example of a perfect number?**
**(a)** 10. **(b)** 6. **(c)** 1. **(d)** 20.

**4. Who was Eratosthanes?**
**(a)** He was the chief librarian, and a mathematician. **(b)** He was a mathematician, and leading doctor. **(c)** He was a teacher and philosopher. **(d)** He was the first to study political sciences.

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

## Short Answer Questions

**1.** What is the name for determining the area of an enclosed space by constructing a square of equivalent area?

**2.** What did Archimedes manage to prove using Euclid's ideas?

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

**4.** Which of Euclid's postulates troubled many of the following generations of mathematicians?

**5.** Which of the following is an example of a postulate that must be accepted in Elements?

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