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This quiz consists of 5 multiple choice and 5 short answer questions through A Sampler of Euler's Number Theory.

## Multiple Choice Questions

**1. Which of the following is false about the modern implications of Euclid's number theory?**
**(a)** Great mathematicians continue to puzzle over some aspects of Euclid's number theory. **(b)** Euclid gave a good idea for how to construct even perfect numbers. **(c)** Euclid's recipe for constructing even perfect numbers is incorrect. **(d)** Whether there are no odd perfect numbers is still not known.

**2. What did the Pythagorean Theorem accomplish for mathematics?**
**(a)** The ability to find square roots. **(b)** The ability to measure angles. **(c)** The concept of constructing useful mathematics. **(d)** The concept of providing a logical proof.

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

**4. What did Archimedes manage to prove using Euclid's ideas?**
**(a)** That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference. **(b)** That the square of a diameter is equal to pi. **(c)** That the value of pi is proportional to the area of the circle. **(d)** That the relationship of area to circumference is really the same as the relationship of radius to diameter.

**5. What is a "depressed cubic"?**
**(a)** A method to solve equations with two variables. **(b)** A method to logically square all the factors in a cubic equation. **(c)** A method to simplify measuring complex geometric forms. **(d)** A method to simpify the x squared value in a cubic equation.

## Short Answer Questions

**1.** Dunham showed that Heron's proof could also be used as which of the following?

**2.** What was the title of Cardano's book which contained the solution to the cubic?

**3.** Who's method did Tartaglia's challenger use in the contest to solve cubic equations?

**4.** In general, what did Euclid's number theory describe?

**5.** What did Dunham consider extraordinary about the Elements?

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