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

## Multiple Choice Questions

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

**2. Which words best describe how solid proofs were developed in Elements?**
**(a)** Inverted scaffold. **(b)** Programmed order. **(c)** Axiomatic framework. **(d)** Simple arguments.

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

**4. What was true about Hippocrates's proof?**
**(a)** The proof was easy if their was advanced technology available. **(b)** The proof was exceedingly difficult and not understood at the time. **(c)** It was useful for circles. **(d)** It was fairly easy and simple.

**5. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?**
**(a)** Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr². **(b)** The area of a triangle is one half the base times the height. **(c)** Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference. **(d)** Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference.

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

**7. Heron's work referred to the work of what other famous scholar?**
**(a)** Hippocrates. **(b)** Euclid. **(c)** Archimedes. **(d)** Thales.

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

**9. Besides being a mathematician, what else other work was Archimedes famous for?**
**(a)** Artist and musician. **(b)** Politician. **(c)** Inventor and scientist. **(d)** Doctor and writer,

**10. Who was Heron?**
**(a)** A philosopher from Greece. **(b)** A politician from Rome. **(c)** A physician from the far East. **(d)** A matematician from Alexanderia.

**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. What does the Pythagorean Theorem state?**
**(a)** For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs. **(b)** For any right triangle the diagonal side is equal to the sum of the legs. **(c)** For any triangle the sum of the legs squared is equal to the length of the hypotenuse. **(d)** For any triangle the sqaured sum of the legs is equal to half the hypotenuse.

**13. When was the work of these early thinkers rediscovered again in history?**
**(a)** In the 20th century. **(b)** In the 18th century. **(c)** In the Elizabethian age. **(d)** In the Renaissance.

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

**15. What did Heron's advances put into historical perspective for Dunham?**
**(a)** A shift in information flow that ignored socioeconomic order. **(b)** A shift in learning across continents. **(c)** A change in learning foundations in the ancient scholarly universities. **(d)** A change in political theory across the globe.

## Short Answer Questions

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

**2.** Which of the following is false about the modern implications of Euclid's number theory?

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

**4.** Who acted as the gate keepers of knowledge?

**5.** Which of the following was an important proposition given by Euclid's number theory?

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