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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. What did Ferdinand Lindeman prove in 1882?
(a) That the square root of the hypotenuse of a right triangle can not be found.
(b) That the square of a circle can not be found with a compass and a straight-edge.
(c) It is impossible to find the square of a semicircle.
(d) It is possible to find the square of a circle.

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

3. Who challenged Tartaglia to a contest to solve cubic equations?
(a) Cardano.
(b) Pacioli.
(c) del Ferro.
(d) Fior.

4. What did Dunham discuss for many pages in this chapter?
(a) Heron's complicated proof.
(b) Heron's political tendancy.
(c) Heron's religious beliefs-
(d) Heron's origins of the universe.

5. Heron devised which of the following methods?
(a) A way to determine the volume in a sphere.
(b) A way to apply mathematics to public health.
(c) A way to solve binomial equations.
(d) A way to determine the area of a triangle.

Short Answer Questions

1. How many definitions were stated in Elements?

2. Which of the following best describes Archimedes as discussed by Dunham?

3. Where did Hippocrates come from?

4. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?

5. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

Short Essay Questions

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

2. What was Euclid's definition of composite and perfect numbers?

3. What did Dunham explain about the shift in learning from the West to the East?

4. What did Dunham describe in the epilogue of the chapter?

5. Describe the contents of Cardano's book.

6. Who was Luca Pacioli, and what controversy was sparked over his writings?

7. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?

8. How did Archimedes find a number value for pi?

9. Why did Euclid's postulate on parallel lines trouble mathematicians for centuries?

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

(see the answer keys)

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