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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. Which of the following is true in modern math about twin primes?**
**(a)** Their sum is always another prime number. **(b)** We don't know if they are finite or infinite. **(c)** They are not considered whole numbers. **(d)** They are infinite.

**2. 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.

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

**4. Which of the following was NOT true about Archimedes, according to Dunham?**
**(a)** He died as a soldier. **(b)** Archimedes died because he refused to follow orders until he completed a math problem. **(c)** His death was described as being by the hands of a Roman invader. **(d)** He died during the fall of Syracuse.

**5. What was the title of Cardano's book which contained the solution to the cubic?**
**(a)** Tarsisia. **(b)** Ars Magna. **(c)** La Magnifica. **(d)** Elements.

**6. 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.

**7. What is true about prime numbers?**
**(a)** Prime numbers can never be an odd number. **(b)** That for every group of prime numbers, there exists at least one more prime. **(c)** Prime numbers are not divisible by other numbers. **(d)** Prime numbers can not exist in a finite series.

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

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

**10. What did Euclid do in his 48th proposition?**
**(a)** Euclid proved the converse of the Pythagorean Theorem. **(b)** Euclid demonstrated the faults of the Pythagorean Theorem. **(c)** Euclid proved the Pythagorean Theorem. **(d)** Euclid demonstrated how to use the Pythagorean Theorem.

**11. Which of Euclid's postulates troubled many of the following generations of mathematicians?**
**(a)** Euclid's postulate on creating an arc. **(b)** Euclid's postulate on right triangles. **(c)** Euclid's proof on right triangles. **(d)** Euclid's postulate on parallel lines.

**12. Where was Archimedes born?**
**(a)** Olympia. **(b)** Athens. **(c)** Rome. **(d)** Sicily.

**13. Which of the following was true about Cardano, according to Dunham?**
**(a)** He had three wives. **(b)** He was a priest. **(c)** He was not a mathematician. **(d)** He was jailed for heresy.

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

**15. What was most useful about finding the square of a shape, before Hippocrates?**
**(a)** It was useful in determining the distance between two points. **(b)** It was useful in finding the area of circles. **(c)** It was useful in finding the area of oddly shaped pieces of land. **(d)** It was useful in creating simple elevation maps,

## Short Answer Questions

**1.** After working on pi, what did Archimedes continue with in his study of mathematics?

**2.** After Hippocrates, what shape did the Greeks attempt to square without success?

**3.** What was the bases of Hippocrates's proof ?

**4.** Who was Neil's Abel?

**5.** What did Euclid state about pi in Elements?

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