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

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

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

4. Which of the following was NOT one of the basic definitions in Elements?
(a) Line.
(b) Straight Line.
(c) Right angles.
(d) Parabola.

5. What did Dunham consider extraordinary about the Elements?
(a) The content was not based on previous authors' work.
(b) How geometric proofs were presented.
(c) The content was totally unique.
(d) How Hippocrates ordered the book.

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

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

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

9. What did the Pythagorean Theorem accomplish for mathematics?
(a) The concept of constructing useful mathematics.
(b) The concept of providing a logical proof.
(c) The ability to find square roots.
(d) The ability to measure angles.

10. What was Euclid's definition of a prime number?
(a) Numbers which do not, and can not, contain a perfect number.
(b) Numbers which can only be divided by themselves and 1.
(c) Numbers which are divisible by 2.
(d) Numbers which contain an infinite number of composite numbers.

11. In what century did Archimedes live?
(a) First century A.D,
(b) Twelthf century A.D.
(c) Third century B.C.
(d) Nineteeth century A.D.

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

13. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to connect any two points with a line and make a circle.
(b) It is possible to draw an arc with any three points.
(c) It is possible to draw a circle that contains no lines.
(d) It is possible to draw a straight line between an infinite number of points.

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

15. Where was Archimedes born?
(a) Rome.
(b) Olympia.
(c) Athens.
(d) Sicily.

Short Answer Questions

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

2. Heron devised which of the following methods?

3. Who was the author of the book Elements?

4. What is true about prime numbers?

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

(see the answer keys)

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