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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?**
**(a)** Square root. **(b)** Quadrature. **(c)** Cubation. **(d)** Triangulation.

**2. How did Archimedes demonstrate his theory of pi?**
**(a)** He demonstrated that the area of the circle is never equal to the area of the triangle. **(b)** He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it. **(c)** He demonstrated that the area of the circle is always greater than the area of the triangle. **(d)** He demonstrated that the area of the circle is never less than the area of the triangle.

**3. What did Dunham discuss for many pages in this chapter?**
**(a)** Heron's complicated proof. **(b)** Heron's political tendancy. **(c)** Heron's origins of the universe. **(d)** Heron's religious beliefs-

**4. Which of the following was NOT one of Gauss' discoveries?**
**(a)** That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees. **(b)** "Non-euclidean" geometry. **(c)** That angles in a triangles can not add up to more than 180 degrees. **(d)** That under Euclid's definition parallel lines can intersect.

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

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

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

**8. According to Dunham, who was most able to collect knowledge from around the globe?**
**(a)** Greek philosophers. **(b)** Greek tradesman. **(c)** Roman emporers. **(d)** Arabian scholars.

**9. In general, what did Euclid's number theory describe?**
**(a)** The nature of whole numbers. **(b)** The nature of measuring geometry. **(c)** The relationship of decimals to integers. **(d)** The relationship of fractions to decimals.

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

**11. Which of the following becomes an important definition in mathematics that was first presented in Elements?**
**(a)** Parallel line. **(b)** Intersection. **(c)** 180 degree angle. **(d)** Circle.

**12. Who wrote a treatise that supposed that cubic equations may be impossible to solve?**
**(a)** Scipione del Ferro. **(b)** Luca Pacioli. **(c)** Niccolo Fontana. **(d)** Gerolamo Cardano.

**13. In what century did Archimedes live?**
**(a)** First century A.D, **(b)** Twelthf century A.D. **(c)** Nineteeth century A.D. **(d)** Third century B.C.

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

**15. What did Dunham consider extraordinary about the Elements?**
**(a)** The content was totally unique. **(b)** The content was not based on previous authors' work. **(c)** How Hippocrates ordered the book. **(d)** How geometric proofs were presented.

## Short Answer Questions

**1.** Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

**2.** As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

**3.** Who asked Tartaglia for his solution to cubic equations?

**4.** Which of the following was true about Cardano, according to Dunham?

**5.** How many definitions were stated in Elements?

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