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

2. 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.

3. What does the Pythagorean Theorem state?
(a) For any right triangle the square of the diagonal side is equal to the sum of the squares of the two legs.
(b) For any right triangle the diagonal side is equal to the sum of the legs.
(c) For any triangle the sum of the legs squared is equal to the length of the hypotenuse.
(d) For any triangle the sqaured sum of the legs is equal to half the hypotenuse.

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

5. What instruments did the Greeks use to square a shape?
(a) A sphere and ruler.
(b) A small grid.
(c) A compass and a ruled straight-edge.
(d) A pendulum.

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

7. Heron devised which of the following methods?
(a) A way to apply mathematics to public health.
(b) A way to solve binomial equations.
(c) A way to determine the volume in a sphere.
(d) A way to determine the area of a triangle.

8. Who asked Tartaglia for his solution to cubic equations?
(a) Fontana.
(b) Fior,
(c) Cardano.
(d) Pacioli.

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

10. After Hippocrates, what shape did the Greeks attempt to square without success?
(a) Hemisphere.
(b) Circle.
(c) Parallelogram.
(d) Pentagon.

11. What did Euclid do in his 48th proposition?
(a) Euclid proved the Pythagorean Theorem.
(b) Euclid demonstrated how to use the Pythagorean Theorem.
(c) Euclid demonstrated the faults of the Pythagorean Theorem.
(d) Euclid proved the converse of the Pythagorean Theorem.

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

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

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

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

Short Answer Questions

1. What was known about pi, during Archimedes' time?

2. What was the title of Cardano's book which contained the solution to the cubic?

3. What did Apollonius work with in mathematics?

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

5. Who's method did Tartaglia's challenger use in the contest to solve cubic equations?

(see the answer keys)

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