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This quiz consists of 5 multiple choice and 5 short answer questions through Euclid and the Infinitude of Primes.

## Multiple Choice Questions

**1. According to Euclid, when is a triangle a right triangle?**
**(a)** When a triangle does not have a side which can be considered a hypotenuse. **(b)** When a triangle has a side whose square is the sum of the squares of the two legs. **(c)** When a triangle has three sides whose squares are equal to the area of the triangle. **(d)** When a triangle can be constructed with three unequal sides.

**2. What was the bases of Hippocrates's proof ?**
**(a)** Properties of triangles and semicircles. **(b)** Properties of squares and cubes. **(c)** Properties of area to volume measurements. **(d)** Properties of points and lines.

**3. 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)** Numbers from one to ten are only divisible by composite numbers. **(d)** Any even number is divisible by 3.

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

**5. What does the Pythagorean Theorem state?**
**(a)** For any triangle the sqaured sum of the legs is equal to half the hypotenuse. **(b)** For any triangle the sum of the legs squared is equal to the length of the hypotenuse. **(c)** For any right triangle the diagonal side is equal to the sum of the legs. **(d)** For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs.

## Short Answer Questions

**1.** In Elements, how many postulates must be accepted as given?

**2.** Which of the following becomes an important definition in mathematics that was first presented in Elements?

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

**4.** What did Euclid do in his 48th proposition?

**5.** Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

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