Journey Through Genius: The Great Theorems of Mathematics Test | Mid-Book Test - Easy

William Dunham (mathematician)
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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. Which mathematician was first to take the challenge to solve cubic equations?
(a) Tartaglia.
(b) Scipione del Ferro.
(c) Luca Pacioli.
(d) Niccolo Fontana.

2. What provided most of the content in the book Elements?
(a) Notions.
(b) Postulates.
(c) Hypotheses.
(d) Propositions.

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

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

5. Which of the following were an example of twin primes?
(a) 11 and 13.
(b) 2 and 6.
(c) 15 and 16.
(d) 19 and 22.

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

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

8. In what time period did mathematicians find a solution to cubic equations?
(a) Fifteen century.
(b) Twentieth century.
(c) Seventeeth century.
(d) Thirteenth century.

9. Which of the following was one of Euclid's great theorems?
(a) There exists only infinite and whole numbers.
(b) There exists an infinite number of prime numbers.
(c) Prime numbers are more comples than discrete numbers.
(d) There exists an finite number of prime numbers.

10. What was most useful about finding the square of a shape, before Hippocrates?
(a) It was useful in creating simple elevation maps,
(b) It was useful in finding the area of circles.
(c) It was useful in finding the area of oddly shaped pieces of land.
(d) It was useful in determining the distance between two points.

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

12. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) Parallel lines.
(b) Intersection.
(c) 180 degree angle.
(d) Circle.

13. What did Archimedes manage to prove using Euclid's ideas?
(a) That the value of pi is proportional to the area of the circle.
(b) That the relationship of area to circumference is really the same as the relationship of radius to diameter.
(c) That the square of a diameter is equal to pi.
(d) That the area of a circle and the square of its diameter is really the same as the relationship of diameter to circumference.

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

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

Short Answer Questions

1. Who challenged Tartaglia to a contest to solve cubic equations?

2. Which is a geometric concept that humans have been aware of since the dawn of agriculture?

3. Where was Archimedes born?

4. What did Heron's advances put into historical perspective for Dunham?

5. As described by Archimedes, what is always true about he diameter of the circle?

(see the answer keys)

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