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Name: _________________________ | Period: ___________________ |

This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

## Multiple Choice Questions

**1. What was Eratosthanes most famous for?**
**(a)** He showed that there are no even prime numbers. **(b)** He developed a way to navigate using logitude and latitude. **(c)** He developed a simple way to find prime numbers and for determining the circumference of the Earth. **(d)** He showed that the Earth must be a sphere.

**2. What did Dunham claim about Archimedes's determination of a number value for pi?**
**(a)** Archimedes's number was very good, considering he did not have a way to calculate square roots. **(b)** Archimedes's number was not very accurate, considering the technology of his time. **(c)** Archimedes's number was perfectly correct. **(d)** Archimedes's number could have been better if he had understood Euclid's work better,

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

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

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

## Short Answer Questions

**1.** Who was del Ferro's student?

**2.** What did the Pythagorean Theorem accomplish for mathematics?

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

**4.** How do we know about Hippocrates proofs and theorems?

**5.** Who was Eratosthanes?

## Short Essay Questions

**1.** Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

**2.** Explain what Archimedes went on to study after the circle, and what was Dunham's opinion of this work.

**3.** How many definitions were in Euclid's book? List some of the definitions he included.

**4.** Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

**5.** What did Dunham explain about the shift in learning from the West to the East?

**6.** How did Archimedes find a number value for pi?

**7.** What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

**8.** Describe in two sentences Archimedes's method for determining circular area.

**9.** Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.

**10.** According the Dunham, how did Euclid prove his theory on the infinitude of primes?

This section contains 1,006 words(approx. 4 pages at 300 words per page) |