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. How did Lindeman prove his conclusion?
(a) Lindeman proved that some numbers are constructable without the use of a compass.
(b) Lindeman proved that all numbers are constructable with a compass and ruler.
(c) Lindeman proved that some numbers are not constructable with only a compass and straight-edge.
(d) Lindeman proved that square roots are irrational numbers.

2. What range of values did Archimedes determine for pi?
(a) Between 3 10/11 and 3 1/7.
(b) Between 3 and 3 1/2.
(c) Between 3 1/2 and 3 5/8.
(d) Between 3 and 4.

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

4. Which was true of Euclid's number theory?
(a) It was incorrect, as proved by Plato.
(b) It has been proven too basic to be useful.
(c) It was proven to the true by Hippocrates.
(d) It has an impact on modern math.

5. In Elements, how many postulates must be accepted as given?
(a) Eighteen.
(b) Five.
(c) Twenty-two.
(d) Twelve,

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

7. Who was Neil's Abel?
(a) He proved that to solve a quartic equation, one must use more than algebra.
(b) He demonstrated that Cardano's solution to the cubic was incorrect,
(c) He proved that quintic equations cannot be solved using algebra.
(d) He demonstrated the modern version of the Pythagorean Theorem.

8. Which city was the center of thinking and learning in Third century BC?
(a) Athens.
(b) Rome.
(c) Olympia.
(d) Alexandria.

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

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

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

12. Which words best describe how solid proofs were developed in Elements?
(a) Inverted scaffold.
(b) Simple arguments.
(c) Axiomatic framework.
(d) Programmed order.

13. 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 radius and the other leg equal to the circle's diameter.
(b) 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.
(c) 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.
(d) 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.

14. Where did Hippocrates come from?
(a) Rome.
(b) Athens.
(c) Constinople.
(d) Chios.

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

Short Answer Questions

1. According to Euclid, when is a triangle a right triangle?

2. Which of the following is an example of a perfect number?

3. Which of the following was one of Euclid's great theorems?

4. What did Euclid state about pi in Elements?

5. How many definitions were stated in Elements?

(see the answer keys)

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