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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. What range of values did Archimedes determine for pi?**
**(a)** Between 3 10/11 and 3 1/7. **(b)** Between 3 and 4. **(c)** Between 3 1/2 and 3 5/8. **(d)** Between 3 and 3 1/2.

**2. Why did Cardano take an oath to secrecy?**
**(a)** It was the only way to get his book published. **(b)** It was the only way to get Tartaglia's solution to cubic equations. **(c)** It was to the only way to win the contest with Fior, **(d)** It was the only way he could become a priest,

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

**4. How do we know about Hippocrates proofs and theorems?**
**(a)** His books and publications. **(b)** What is known from archived documents of his time. **(c)** What we know is from references of later mathematicians. **(d)** Mathematicians rewrote all of his proofs after his death,

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

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

**7. In Elements, how many postulates must be accepted as given?**
**(a)** Five. **(b)** Eighteen. **(c)** Twelve, **(d)** Twenty-two.

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

**9. According to Euclid, when is a triangle a right triangle?**
**(a)** When a triangle can be constructed with three unequal sides. **(b)** When a triangle has three sides whose squares are equal to the area of the triangle. **(c)** When a triangle has a side whose square is the sum of the squares of the two legs. **(d)** When a triangle does not have a side which can be considered a hypotenuse.

**10. What shape was NOT demonstrated in the Elements as having a relationship to other shapes?**
**(a)** Triangle. **(b)** Hexagon. **(c)** Hyperbola. **(d)** Pentagon.

**11. Who challenged Tartaglia to a contest to solve cubic equations?**
**(a)** Fior. **(b)** Pacioli. **(c)** Cardano. **(d)** del Ferro.

**12. Who asked Tartaglia for his solution to cubic equations?**
**(a)** Pacioli. **(b)** Cardano. **(c)** Fontana. **(d)** Fior,

**13. Where did Hippocrates come from?**
**(a)** Chios. **(b)** Athens. **(c)** Rome. **(d)** Constinople.

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

**15. Which of the following is true about pi, as described by Dunham.**
**(a)** The measurement of pi should not have been so difficult for Archimedes to demonstrate. **(b)** The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics. **(c)** The measurement of pi is a challenge that continues into modern mathematics. **(d)** The measurement of pi was redetermined after Archimedes's death.

## Short Answer Questions

**1.** Which of the following becomes an important definition in mathematics that was first presented in Elements?

**2.** Heron devised which of the following methods?

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

**4.** What was Hippocrates famous for?

**5.** How did Lindeman prove his conclusion?

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