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

## Multiple Choice Questions

**1. Which of the following is an example of a postulate that must be accepted in Elements?**
**(a)** It is possible to connect any two points with a line and make a circle. **(b)** It is possible to draw an arc with any three points. **(c)** It is possible to draw a straight line between an infinite number of points. **(d)** It is possible to draw a circle that contains no lines.

**2. Which of the following could NOT be included as a step in Euclid's great theorem?**
**(a)** After summation, the new number can be prime or composite. **(b)** Take a finite group of primes and add them together, plus one. **(c)** If a new number is found to be composite, then it must have some prime as a divisor. **(d)** Divide a infinite group of primes by the sum of their composites.

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

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

**5. After working on pi, what did Archimedes continue with in his study of mathematics?**
**(a)** He studied the relationship of sine to cosine. **(b)** He studied the relationship between ratios in triangles. **(c)** He studied the volume to surface area ratios of cubes. **(d)** He studied the volume and surface area of spheres, cones, and cylinders.

**6. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?**
**(a)** del Ferro's method. **(b)** Cardano's method. **(c)** Fontana's method. **(d)** Pacioli's method.

**7. What did Dunham consider extraordinary about the Elements?**
**(a)** The content was totally unique. **(b)** The content was not based on previous authors' work. **(c)** How geometric proofs were presented. **(d)** How Hippocrates ordered the book.

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

**9. Exactly what limit is reached at a quartic equation?**
**(a)** The limit of algebra. **(b)** The limit of the Pythagorean Theorem. **(c)** The limit of the decompressed cubic method. **(d)** The limit of logical geometric proofs.

**10. What was the same about Apollonius and Erosthanes?**
**(a)** They both studied the Universe. **(b)** They both calculated the circumference of the earth. **(c)** They were both mathematicians. **(d)** They were both born in the same year.

**11. Where was the modern number system developed?**
**(a)** In the West. **(b)** In ancient Rome. **(c)** In the East. **(d)** In ancient Alexanderia.

**12. What was known about pi, during Archimedes' time?**
**(a)** Nothing, the concept of pi was unknown. **(b)** That it was never the same number value for a given circle. **(c)** That it could not be assigned a relationship between measurements in a circle. **(d)** That is was the relationship between the diameter and circumference of a circle.

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

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

**15. 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 does not have a side which can be considered a hypotenuse. **(c)** When a triangle has a side whose square is the sum of the squares of the two legs. **(d)** When a triangle has three sides whose squares are equal to the area of the triangle.

## Short Answer Questions

**1.** Which words best describe how solid proofs were developed in Elements?

**2.** What provided most of the content in the book Elements?

**3.** "Straight lines in the same plane that will never meet if extended forever" is a definition of what?

**4.** What did Archimedes manage to prove using Euclid's ideas?

**5.** Who was Eratosthanes?

This section contains 772 words(approx. 3 pages at 300 words per page) |