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. Why did Cardano take an oath to secrecy?
(a) It was the only way to get his book published.
(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 to the only way to win the contest with Fior,

2. Which of the following is false about the modern implications of Euclid's number theory?
(a) Whether there are no odd perfect numbers is still not known.
(b) Euclid gave a good idea for how to construct even perfect numbers.
(c) Euclid's recipe for constructing even perfect numbers is incorrect.
(d) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.

3. 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 hypotenuse 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 diameter 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 radius and the other leg equal to the circle's circumference.

4. 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) A suggested method to depress all complex geometry.
(d) An alegrabic solution to quintic equations,

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

6. How many sides did the pentadecagon have, as presented by Euclid?
(a) Twenty.
(b) Five.
(c) Ten.
(d) Fifteen.

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

8. Which of the following is an example of a perfect number?
(a) 1.
(b) 20.
(c) 6.
(d) 10.

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

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

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

12. What did Heron's advances put into historical perspective for Dunham?
(a) A shift in learning across continents.
(b) A change in learning foundations in the ancient scholarly universities.
(c) A change in political theory across the globe.
(d) A shift in information flow that ignored socioeconomic order.

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

14. Which of the following was NOT one of the things Dunham claimed was ingenious about Euclid's proof of the Pythagorean theorem?
(a) Euclid used propositions about similar angles and parallel lines.
(b) Euclid constructed squares on the sides of right triangles.
(c) Euclid used his own axioms and propositions to show relationships,
(d) Euclid stated that the diagonal hypotenuse of a right triangle is equal to the sums of the squares of the two legs.

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

Short Answer Questions

1. Which words best describe how solid proofs were developed in Elements?

2. When was the work of these early thinkers rediscovered again in history?

3. What was most useful about finding the square of a shape, before Hippocrates?

4. What did most of Heron's work deal with?

5. What did Dunham claim about Archimedes's determination of a number value for pi?

(see the answer keys)

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