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

Multiple Choice Questions

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

2. What is a "depressed cubic"?
(a) A method to simplify measuring complex geometric forms.
(b) A method to logically square all the factors in a cubic equation.
(c) A method to simpify the x squared value in a cubic equation.
(d) A method to solve equations with two variables.

3. Which of the following can not be solved using algebra?
(a) Geometric equation.
(b) Quadratic equation.
(c) Triangulation.
(d) Quintic equation.

4. Which is a geometric concept that humans have been aware of since the dawn of agriculture?
(a) Metric system.
(b) Volume.
(c) Area.
(d) Gravity.

5. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?
(a) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference.
(b) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.
(c) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter.
(d) Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference.

6. Who was the author of the book Elements?
(a) Einstein.
(b) Lindemann.
(c) Euclid.
(d) Hippocrates.

7. Which of the following was NOT defined by Euclid?
(a) Odd numbers.
(b) Even numbers.
(c) Nominal numbers.
(d) Whole numbers.

8. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?
(a) Composite numbers.
(b) Discrete numbers.
(c) Even numbers.
(d) Perfect numbers.

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

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

11. What were the proofs in Elements based on?
(a) Lindeman's method.
(b) Novel notions.
(c) Ancient greek geometry.
(d) Basic definitions.

12. How many definitions were stated in Elements?
(a) Twenty-three.
(b) Five.
(c) Thirty.
(d) Eighteen.

13. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Thales.
(b) Hippocrates.
(c) Aristotle.
(d) Pythagoras.

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

15. What was true about Heron's theorem as described by Dunham?
(a) It was to determine the volume of a sphere without measuring the circumference.
(b) It was to solve equations were only two varibles are known.
(c) It was to determine the area of a circle by measuring a right triangle inside the circle.
(d) It was to find the area of a triangle when only the length of the sides are known.

Short Answer Questions

1. Where did Hippocrates come from?

2. Who was Eratosthanes?

3. What was the same about Apollonius and Erosthanes?

4. Which of the following were an example of twin primes?

5. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?

(see the answer keys)

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