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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. What was Euclid's definition of a prime number?**
**(a)** Numbers which are divisible by 2. **(b)** Numbers which do not, and can not, contain a perfect number. **(c)** Numbers which contain an infinite number of composite numbers. **(d)** Numbers which can only be divided by themselves and 1.

**2. According to Euclid, when is a triangle a right triangle?**
**(a)** When a triangle has a side whose square is the sum of the squares of the two legs. **(b)** When a triangle does not have a side which can be considered a hypotenuse. **(c)** When a triangle can be constructed with three unequal sides. **(d)** When a triangle has three sides whose squares are equal to the area of the triangle.

**3. What does the Pythagorean Theorem state?**
**(a)** For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs. **(b)** For any right triangle the diagonal side is equal to the sum of the legs. **(c)** For any triangle the sum of the legs squared is equal to the length of the hypotenuse. **(d)** For any triangle the sqaured sum of the legs is equal to half the hypotenuse.

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

**5. What instruments did the Greeks use to square a shape?**
**(a)** A sphere and ruler. **(b)** A small grid. **(c)** A compass and a ruled straight-edge. **(d)** A pendulum.

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

**7. Heron devised which of the following methods?**
**(a)** A way to apply mathematics to public health. **(b)** A way to solve binomial equations. **(c)** A way to determine the volume in a sphere. **(d)** A way to determine the area of a triangle.

**8. Who asked Tartaglia for his solution to cubic equations?**
**(a)** Fontana. **(b)** Fior, **(c)** Cardano. **(d)** Pacioli.

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

**10. After Hippocrates, what shape did the Greeks attempt to square without success?**
**(a)** Hemisphere. **(b)** Circle. **(c)** Parallelogram. **(d)** Pentagon.

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

**12. What did Plato use his inspiration from Euclid for?**
**(a)** To create a new theorem of algebra. **(b)** To classify geometric shapes by their complexity. **(c)** To prove Euclid's number theory was incorrect. **(d)** To construct his theory on the shape of the Universe.

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

**14. What allowed Cardano to justify publishing his book?**
**(a)** He was dead, and the book was really published by his student. **(b)** He was punished as a heretic, **(c)** He found Fior's documents which spoke against Tartaglia. **(d)** He found del Ferro's orgininal solution to the cubic.

**15. Who was Eratosthanes?**
**(a)** He was a teacher and philosopher. **(b)** He was the first to study political sciences. **(c)** He was the chief librarian, and a mathematician. **(d)** He was a mathematician, and leading doctor.

## Short Answer Questions

**1.** What was known about pi, during Archimedes' time?

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

**3.** What did Apollonius work with in mathematics?

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

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

This section contains 712 words(approx. 3 pages at 300 words per page) |