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. After working on pi, what did Archimedes continue with in his study of mathematics?
(a) He studied the volume and surface area of spheres, cones, and cylinders.
(b) He studied the relationship of sine to cosine.
(c) He studied the volume to surface area ratios of cubes.
(d) He studied the relationship between ratios in triangles.

2. When was the work of these early thinkers rediscovered again in history?
(a) In the Elizabethian age.
(b) In the Renaissance.
(c) In the 20th century.
(d) In the 18th century.

3. Which shapes as described by Euclid, inspired the Greek philosopher Plato?
(a) Triangles.
(b) Manifolds.
(c) Regular polyhedrons.
(d) Spheres and cones.

4. What did Euclid state about pi in Elements?
(a) The proportion of diameter to area is never equal.
(b) The proportion of area to circumference is never equal.
(c) There is a constant relationship between the area of a circle and the square of its diameter.
(d) There is no relationship between the area of a circle and its circumference.

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

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

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

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

9. 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 parallel lines.
(c) Euclid's postulate on right triangles.
(d) Euclid's postulate on creating an arc.

10. 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 circumference.
(b) 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.
(c) 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.
(d) 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.

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

12. Besides being a mathematician, what else other work was Archimedes famous for?
(a) Artist and musician.
(b) Politician.
(c) Inventor and scientist.
(d) Doctor and writer,

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

14. 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) Take a finite group of primes and add them together, plus one.
(c) Divide a infinite group of primes by the sum of their composites.
(d) After summation, the new number can be prime or composite.

15. Dunham showed that Heron's proof could also be used as which of the following?
(a) A proof of Archimedes' number theory.
(b) A proof of Hippocrates' squared areas.
(c) A proof of the Pythagorean Theorem.
(d) A proof of Euclid's number theory

Short Answer Questions

1. What was the same about Apollonius and Erosthanes?

2. Which is a geometric concept that humans have been aware of since the dawn of agriculture?

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

4. Who acted as the gate keepers of knowledge?

5. What name did Euclid give for numbers that could be divided by numbers other than themselves and one?

(see the answer keys)

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