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. Numbers whose divisor add up to itself, was considered which type of number according to Euclid?
(a) Even number.
(b) Composite number.
(c) Nominal number.
(d) Perfect number.

2. As described by Archimedes, what is always true about he diameter of the circle?
(a) It's equal to pi.
(b) It's always proportional to its circumference.
(c) It's never proportional to its circumference.
(d) It's equal to the square of the radius.

3. What did most of Heron's work deal with?
(a) Practical mathematics applications.
(b) Theoretical mathematics.
(c) Practical solutions to public problems.
(d) Philosophical questions on the origins of the universe.

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

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

6. What did Plato use his inspiration from Euclid for?
(a) To prove Euclid's number theory was incorrect.
(b) To classify geometric shapes by their complexity.
(c) To create a new theorem of algebra.
(d) To construct his theory on the shape of the Universe.

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

8. What was Hippocrates's great advance to mathematics?
(a) He showed how to square a circle.
(b) He showed how to find the angles in a right triangle.
(c) He showed how to simplify the area of a triangle.
(d) He showed how to square a figure with curved sides.

9. According to Dunham, who was most able to collect knowledge from around the globe?
(a) Greek tradesman.
(b) Greek philosophers.
(c) Roman emporers.
(d) Arabian scholars.

10. Which of the following could NOT be included as a step in Euclid's great theorem?
(a) If a new number is found to be composite, then it must have some prime as a divisor.
(b) After summation, the new number can be prime or composite.
(c) Take a finite group of primes and add them together, plus one.
(d) Divide a infinite group of primes by the sum of their composites.

11. Which is one of the common notions presented in Elements?
(a) "Things with are equal have an inverse that is equal."
(b) "The inverse of a line makes a circle."
(c) "Points with equal values can be connected with a line of equal value."
(d) "Things which are equal to the same thing are also equal to each other."

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

13. What was true about Heron's theorem as described by Dunham?
(a) It was to find the area of a triangle when only the length of the sides are known.
(b) It was to determine the volume of a sphere without measuring the circumference.
(c) It was to determine the area of a circle by measuring a right triangle inside the circle.
(d) It was to solve equations were only two varibles are known.

14. 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 there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.
(d) That under Euclid's definition parallel lines can intersect.

15. Which of the following becomes an important definition in mathematics that was first presented in Elements?
(a) Circle.
(b) 180 degree angle.
(c) Intersection.
(d) Parallel line.

Short Answer Questions

1. How many sides did the pentadecagon have, as presented by Euclid?

2. Which of the following was true about Cardano, according to Dunham?

3. Who asked Tartaglia for his solution to cubic equations?

4. How did Archimedes arrive at a number value for pi?

5. Which of the following is an example of a postulate that must be accepted in Elements?

(see the answer keys)

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