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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

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

2. What was the bases of Hippocrates's proof ?
(a) Properties of points and lines.
(b) Properties of squares and cubes.
(c) Properties of area to volume measurements.
(d) Properties of triangles and semicircles.

3. Who was del Ferro's student?
(a) Niccolo Fontana.
(b) Gerolamo Cardano.
(c) Luca Pacioli.
(d) Antonio Fior.

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

5. What allowed Cardano to justify publishing his book?
(a) He was dead, and the book was really published by his student.
(b) He found Fior's documents which spoke against Tartaglia.
(c) He found del Ferro's orgininal solution to the cubic.
(d) He was punished as a heretic,

Short Answer Questions

1. What does the Pythagorean Theorem state?

2. Heron's work referred to the work of what other famous scholar?

3. Besides being a mathematician, what else other work was Archimedes famous for?

4. Which shapes as described by Euclid, inspired the Greek philosopher Plato?

5. Who was Neil's Abel?

Short Essay Questions

1. Describe what the Egyptians knew about geometry and triangles before Hippocrates.

2. Describe what Gauss discovered according to Dunham.

3. Describe what is quadrature and why it was useful in the time of Hippocrates.

4. Describe Lindeman's work on the square of a circle, and state what he discovered.

5. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

6. Describe the events that follow del Ferro's death between Fior and Tartaglia.

7. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.

8. Describe the ancient city Alexandria and name a few of its third century geniuses.

9. How many definitions were in Euclid's book? List some of the definitions he included.

10. Describe the contents of Cardano's book.

(see the answer keys)

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