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

**2. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?**
**(a)** Quadrature. **(b)** Cubation. **(c)** Square root. **(d)** Triangulation.

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

**4. What did Hippocrates do that advanced mathematical methods?**
**(a)** He built theorems based on sequencially more complex proofs. **(b)** He created a new ways to disprove theories. **(c)** He proved that mathematics can be applied in a unlogical order. **(d)** He demonstrated that geometry does not have to be based on previous knowledge.

**5. What did Gauss set out to prove?**
**(a)** That the sum of the angles in a triangle is 180 degrees. **(b)** That a right angle is always equal to 90 degrees. **(c)** That Euclid's postulate on straight lines was incorrect. **(d)** That a circle can have less than 360 degrees.

**6. Where was Neil's Abel from?**
**(a)** Norway. **(b)** Ireland. **(c)** Great Britian, **(d)** Finland.

**7. Who was Eratosthanes?**
**(a)** He was the first to study political sciences. **(b)** He was a mathematician, and leading doctor. **(c)** He was the chief librarian, and a mathematician. **(d)** He was a teacher and philosopher.

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

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

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

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

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

**13. That properties of specific shapes were early Egyptians aware of?**
**(a)** Irregular solids. **(b)** Pi and the diameter of a circle. **(c)** Parallelograms. **(d)** Right triangles.

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

**15. Which was true of Euclid's number theory?**
**(a)** It was incorrect, as proved by Plato. **(b)** It was proven to the true by Hippocrates. **(c)** It has been proven too basic to be useful. **(d)** It has an impact on modern math.

## Short Answer Questions

**1.** What was true about Heron's theorem as described by Dunham?

**2.** Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

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

**4.** What did Dunham consider as Archimedes's "masterpiece"?

**5.** As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

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