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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

## Multiple Choice Questions

**1. Which of Euclid's postulates troubled many of the following generations of mathematicians?**
**(a)** Euclid's postulate on parallel lines. **(b)** Euclid's postulate on creating an arc. **(c)** Euclid's proof on right triangles. **(d)** Euclid's postulate on right triangles.

**2. Which is one of the common notions presented in Elements?**
**(a)** "Things which are equal to the same thing are also equal to each other." **(b)** "Points with equal values can be connected with a line of equal value." **(c)** "The inverse of a line makes a circle." **(d)** "Things with are equal have an inverse that is equal."

**3. Which was true of Euclid's number theory?**
**(a)** It was incorrect, as proved by Plato. **(b)** It has an impact on modern math. **(c)** It has been proven too basic to be useful. **(d)** It was proven to the true by Hippocrates.

**4. Where did Hippocrates come from?**
**(a)** Constinople. **(b)** Chios. **(c)** Rome. **(d)** Athens.

**5. Heron's work referred to the work of what other famous scholar?**
**(a)** Thales. **(b)** Euclid. **(c)** Hippocrates. **(d)** Archimedes.

## Short Answer Questions

**1.** What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

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

**3.** Which words best describe how solid proofs were developed in Elements?

**4.** What was most useful about finding the square of a shape, before Hippocrates?

**5.** Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

## Short Essay Questions

**1.** What was Euclid's definition of composite and perfect numbers?

**2.** What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

**3.** Who was Luca Pacioli, and what controversy was sparked over his writings?

**4.** Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

**5.** What was already known about circles before Archimedes?

**6.** Describe the connection between Fermat and Euler's work.

**7.** Describe the contents of Cardano's book.

**8.** Explain who was Hippocrates, his contribution to mathematics, and how do we know about him?

**9.** Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

**10.** Give an example of a series who's sum is still unknown.

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