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This quiz consists of 5 multiple choice and 5 short answer questions through Cantor and the Transfinite Realm.

## Multiple Choice Questions

**1. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?**
**(a)** Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference. **(b)** Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference. **(c)** The area of a triangle is one half the base times the height. **(d)** Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr².

**2. What was aleph naught?**
**(a)** A method to determine the sum of a series. **(b)** A symbol to represent the number of items in a set. **(c)** A symbol to state the sum of a series. **(d)** A method to numerate terms.

**3. Where was the modern number system developed?**
**(a)** In the West. **(b)** In ancient Rome. **(c)** In the East. **(d)** In ancient Alexanderia.

**4. What did Gauss set out to prove?**
**(a)** That the sum of the angles in a triangle is 180 degrees. **(b)** That a circle can have less than 360 degrees. **(c)** That a right angle is always equal to 90 degrees. **(d)** That Euclid's postulate on straight lines was incorrect.

**5. 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)** That under Euclid's definition parallel lines can intersect. **(c)** "Non-euclidean" geometry. **(d)** That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.

## Short Answer Questions

**1.** Where does the center of mathematical thinking shift to after Italy?

**2.** What was Euclid's definition of a prime number?

**3.** Which phrase best describes Newton as a student at Cambridge?

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

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

This section contains 464 words(approx. 2 pages at 300 words per page) |