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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. Who acted as the gate keepers of knowledge?**
**(a)** Greek philosophers. **(b)** Arabian scholars. **(c)** Roman emporers. **(d)** Greek tradesman.

**2. Which shapes as described by Euclid, inspired the Greek philosopher Plato?**
**(a)** Spheres and cones. **(b)** Regular polyhedrons. **(c)** Triangles. **(d)** Manifolds.

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

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

**5. 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 right triangles. **(c)** Euclid's proof on right triangles. **(d)** Euclid's postulate on creating an arc.

**6. After working on pi, what did Archimedes continue with in his study of mathematics?**
**(a)** He studied the relationship of sine to cosine. **(b)** He studied the relationship between ratios in triangles. **(c)** He studied the volume and surface area of spheres, cones, and cylinders. **(d)** He studied the volume to surface area ratios of cubes.

**7. Who was Heron?**
**(a)** A philosopher from Greece. **(b)** A politician from Rome. **(c)** A physician from the far East. **(d)** A matematician from Alexanderia.

**8. 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.

**9. What did most of Heron's work deal with?**
**(a)** Philosophical questions on the origins of the universe. **(b)** Practical mathematics applications. **(c)** Practical solutions to public problems. **(d)** Theoretical mathematics.

**10. Which of the following best describes Cardano's character?**
**(a)** Flirtacious. **(b)** Arrogant. **(c)** Religious. **(d)** Eccentric.

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

**12. What did Ferdinand Lindeman prove in 1882?**
**(a)** It is impossible to find the square of a semicircle. **(b)** It is possible to find the square of a circle. **(c)** That the square of a circle can not be found with a compass and a straight-edge. **(d)** That the square root of the hypotenuse of a right triangle can not be found.

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

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

**15. What was Hippocrates's great advance to mathematics?**
**(a)** He showed how to simplify the area of a triangle. **(b)** He showed how to square a circle. **(c)** He showed how to square a figure with curved sides. **(d)** He showed how to find the angles in a right triangle.

## Short Answer Questions

**1.** What was true about Hippocrates's proof?

**2.** Which of the following could NOT be included as a step in Euclid's great theorem?

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

**4.** What was Hippocrates famous for?

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

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