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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

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

**2. When was the work of these early thinkers rediscovered again in history?**
**(a)** In the Elizabethian age. **(b)** In the Renaissance. **(c)** In the 20th century. **(d)** In the 18th century.

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

**4. 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.

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

**6. Which of the following is an example of a postulate that must be accepted in Elements?**
**(a)** It is possible to draw an arc with any three points. **(b)** It is possible to draw a straight line between an infinite number of points. **(c)** It is possible to connect any two points with a line and make a circle. **(d)** It is possible to draw a circle that contains no lines.

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

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

**9. 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 parallel lines. **(c)** Euclid's postulate on right triangles. **(d)** Euclid's postulate on creating an arc.

**10. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?**
**(a)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference. **(b)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter. **(c)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference. **(d)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.

**11. Which mathematician was first to take the challenge to solve cubic equations?**
**(a)** Scipione del Ferro. **(b)** Luca Pacioli. **(c)** Niccolo Fontana. **(d)** Tartaglia.

**12. Besides being a mathematician, what else other work was Archimedes famous for?**
**(a)** Artist and musician. **(b)** Politician. **(c)** Inventor and scientist. **(d)** Doctor and writer,

**13. Which of the following was NOT one of the basic definitions in Elements?**
**(a)** Straight Line. **(b)** Line. **(c)** Parabola. **(d)** Right angles.

**14. Which of the following could NOT be included as a step in Euclid's great theorem?**
**(a)** If a new number is found to be composite, then it must have some prime as a divisor. **(b)** Take a finite group of primes and add them together, plus one. **(c)** Divide a infinite group of primes by the sum of their composites. **(d)** After summation, the new number can be prime or composite.

**15. Dunham showed that Heron's proof could also be used as which of the following?**
**(a)** A proof of Archimedes' number theory. **(b)** A proof of Hippocrates' squared areas. **(c)** A proof of the Pythagorean Theorem. **(d)** A proof of Euclid's number theory

## Short Answer Questions

**1.** What was the same about Apollonius and Erosthanes?

**2.** Which is a geometric concept that humans have been aware of since the dawn of agriculture?

**3.** What did Dunham claim about Archimedes's determination of a number value for pi?

**4.** Who acted as the gate keepers of knowledge?

**5.** What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

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