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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. What was most useful about finding the square of a shape, before Hippocrates?**
**(a)** It was useful in creating simple elevation maps, **(b)** It was useful in finding the area of oddly shaped pieces of land. **(c)** It was useful in determining the distance between two points. **(d)** It was useful in finding the area of circles.

**2. What was Eratosthanes most famous for?**
**(a)** He showed that the Earth must be a sphere. **(b)** He developed a simple way to find prime numbers and for determining the circumference of the Earth. **(c)** He developed a way to navigate using logitude and latitude. **(d)** He showed that there are no even prime numbers.

**3. Which of the following is true about pi, as described by Dunham.**
**(a)** The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics. **(b)** The measurement of pi should not have been so difficult for Archimedes to demonstrate. **(c)** The measurement of pi was redetermined after Archimedes's death. **(d)** The measurement of pi is a challenge that continues into modern mathematics.

**4. What did Euclid state about pi in Elements?**
**(a)** There is no relationship between the area of a circle and its circumference. **(b)** There is a constant relationship between the area of a circle and the square of its diameter. **(c)** The proportion of diameter to area is never equal. **(d)** The proportion of area to circumference is never equal.

**5. What were the main technique(s) that Euler used to find the sum of the series?**
**(a)** Calculus methods. **(b)** Cubic equations. **(c)** Trigonometry and basic algebra. **(d)** Quadratic sums,

## Short Answer Questions

**1.** What was most noticeable about Euler at a young age?

**2.** In what time period did mathematicians find a solution to cubic equations?

**3.** What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?

**4.** What did most of 19th century mathematics focus on, as highlighted by Dunham?

**5.** Who was Heron?

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