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Name: _________________________ | Period: ___________________ |

This test consists of 15 multiple choice questions and 5 short answer questions.

## Multiple Choice Questions

**1. Which city was the center of thinking and learning in Third century BC?**
**(a)** Alexandria. **(b)** Olympia. **(c)** Athens. **(d)** Rome.

**2. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?**
**(a)** Discrete numbers. **(b)** Even numbers. **(c)** Composite numbers. **(d)** Perfect numbers.

**3. What did Hippocrates do that advanced mathematical methods?**
**(a)** He proved that mathematics can be applied in a unlogical order. **(b)** He demonstrated that geometry does not have to be based on previous knowledge. **(c)** He created a new ways to disprove theories. **(d)** He built theorems based on sequencially more complex proofs.

**4. Exactly what limit is reached at a quartic equation?**
**(a)** The limit of the Pythagorean Theorem. **(b)** The limit of the decompressed cubic method. **(c)** The limit of algebra. **(d)** The limit of logical geometric proofs.

**5. What did Euclid do in his 48th proposition?**
**(a)** Euclid demonstrated how to use the Pythagorean Theorem. **(b)** Euclid proved the converse of the Pythagorean Theorem. **(c)** Euclid proved the Pythagorean Theorem. **(d)** Euclid demonstrated the faults of the Pythagorean Theorem.

**6. As described by Archimedes, what is always true about he diameter of the circle?**
**(a)** It's equal to pi. **(b)** It's always proportional to its circumference. **(c)** It's never proportional to its circumference. **(d)** It's equal to the square of the radius.

**7. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?**
**(a)** 180 degree angle. **(b)** Parallel lines. **(c)** Circle. **(d)** Intersection.

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

**9. What do we know in modern times about Heron?**
**(a)** We know he was an influencial scholar, but we don't know who his students were. **(b)** We know he lived in Rome. **(c)** We know he was a teacher and philosopher but much of his work has been lost. **(d)** We know very little, but much of his work survives.

**10. In Elements, how many postulates must be accepted as given?**
**(a)** Twelve, **(b)** Eighteen. **(c)** Five. **(d)** Twenty-two.

**11. That properties of specific shapes were early Egyptians aware of?**
**(a)** Pi and the diameter of a circle. **(b)** Parallelograms. **(c)** Right triangles. **(d)** Irregular solids.

**12. What was the title of Cardano's book which contained the solution to the cubic?**
**(a)** La Magnifica. **(b)** Ars Magna. **(c)** Tarsisia. **(d)** Elements.

**13. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?**
**(a)** del Ferro's method. **(b)** Fontana's method. **(c)** Pacioli's method. **(d)** Cardano's method.

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

**15. Which of the following is an example of a perfect number?**
**(a)** 1. **(b)** 20. **(c)** 10. **(d)** 6.

## Short Answer Questions

**1.** How many sides did the pentadecagon have, as presented by Euclid?

**2.** Which of the following best describes Cardano's character?

**3.** What instruments did the Greeks use to square a shape?

**4.** Which of the following was NOT one of the basic definitions in Elements?

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

This section contains 575 words(approx. 2 pages at 300 words per page) |