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 the following was NOT one of Gauss' discoveries?
(a) "Non-euclidean" geometry.
(b) That angles in a triangles can not add up to more than 180 degrees.
(c) That under Euclid's definition parallel lines can intersect.
(d) That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.

2. Why did Cardano take an oath to secrecy?
(a) It was to the only way to win the contest with Fior,
(b) It was the only way he could become a priest,
(c) It was the only way to get Tartaglia's solution to cubic equations.
(d) It was the only way to get his book published.

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

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

5. What else, besides a solution to cubic equations, was in Cardano's book?
(a) A proof of the Pythagorean Theorem.
(b) A solution to quartic equations.
(c) An alegrabic solution to quintic equations,
(d) A suggested method to depress all complex geometry.

6. What did Gauss set out to prove?
(a) That a right angle is always equal to 90 degrees.
(b) That the sum of the angles in a triangle is 180 degrees.
(c) That Euclid's postulate on straight lines was incorrect.
(d) That a circle can have less than 360 degrees.

7. Where was Neil's Abel from?
(a) Norway.
(b) Finland.
(c) Ireland.
(d) Great Britian,

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

9. What is a "depressed cubic"?
(a) A method to simplify measuring complex geometric forms.
(b) A method to logically square all the factors in a cubic equation.
(c) A method to solve equations with two variables.
(d) A method to simpify the x squared value in a cubic equation.

10. What was the title of Cardano's book which contained the solution to the cubic?
(a) La Magnifica.
(b) Elements.
(c) Tarsisia.
(d) Ars Magna.

11. According to Euclid, when is a triangle a right triangle?
(a) When a triangle has a side whose square is the sum of the squares of the two legs.
(b) When a triangle does not have a side which can be considered a hypotenuse.
(c) When a triangle can be constructed with three unequal sides.
(d) When a triangle has three sides whose squares are equal to the area of the triangle.

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

13. How many definitions were stated in Elements?
(a) Five.
(b) Twenty-three.
(c) Eighteen.
(d) Thirty.

14. Who was Eratosthanes?
(a) He was a teacher and philosopher.
(b) He was a mathematician, and leading doctor.
(c) He was the first to study political sciences.
(d) He was the chief librarian, and a mathematician.

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

Short Answer Questions

1. Which mathematician was first to take the challenge to solve cubic equations?

2. Who was the first of ancient philosophers to consider why geometric properties existed?

3. Dunham showed that Heron's proof could also be used as which of the following?

4. In general, what did Euclid's number theory describe?

5. Which of the following is false about the modern implications of Euclid's number theory?

(see the answer keys)

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