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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?**
**(a)** Even number. **(b)** Composite number. **(c)** Nominal number. **(d)** Perfect number.

**2. 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.

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

**4. Which of the following was one of Euclid's great theorems?**
**(a)** There exists an finite number of prime numbers. **(b)** Prime numbers are more comples than discrete numbers. **(c)** There exists only infinite and whole numbers. **(d)** There exists an infinite number of prime numbers.

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

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

**7. What did Archimedes manage to prove using Euclid's ideas?**
**(a)** That the square of a diameter is equal to pi. **(b)** That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference. **(c)** That the value of pi is proportional to the area of the circle. **(d)** That the relationship of area to circumference is really the same as the relationship of radius to diameter.

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

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

**10. 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)** After summation, the new number can be prime or composite. **(c)** Take a finite group of primes and add them together, plus one. **(d)** Divide a infinite group of primes by the sum of their composites.

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

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

**13. What was true about Heron's theorem as described by Dunham?**
**(a)** It was to find the area of a triangle when only the length of the sides are known. **(b)** It was to determine the volume of a sphere without measuring the circumference. **(c)** It was to determine the area of a circle by measuring a right triangle inside the circle. **(d)** It was to solve equations were only two varibles are known.

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

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

## Short Answer Questions

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

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

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

**4.** How did Archimedes arrive at a number value for pi?

**5.** Which of the following is an example of a postulate that must be accepted in Elements?

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