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. 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.

2. Who was del Ferro's student?
(a) Gerolamo Cardano.
(b) Luca Pacioli.
(c) Antonio Fior.
(d) Niccolo Fontana.

3. What did Dunham claim about Archimedes's determination of a number value for pi?
(a) Archimedes's number was not very accurate, considering the technology of his time.
(b) Archimedes's number was very good, considering he did not have a way to calculate square roots.
(c) Archimedes's number was perfectly correct.
(d) Archimedes's number could have been better if he had understood Euclid's work better,

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

5. In general, what did Euclid's number theory describe?
(a) The relationship of decimals to integers.
(b) The nature of whole numbers.
(c) The nature of measuring geometry.
(d) The relationship of fractions to decimals.

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

7. Which is a geometric concept that humans have been aware of since the dawn of agriculture?
(a) Gravity.
(b) Metric system.
(c) Volume.
(d) Area.

8. What provided most of the content in the book Elements?
(a) Postulates.
(b) Propositions.
(c) Hypotheses.
(d) Notions.

9. 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) Great mathematicians continue to puzzle over some aspects of Euclid's number theory.
(c) Euclid gave a good idea for how to construct even perfect numbers.
(d) Whether there are no odd perfect numbers is still not known.

10. What was true about Hippocrates's proof?
(a) It was fairly easy and simple.
(b) The proof was exceedingly difficult and not understood at the time.
(c) The proof was easy if their was advanced technology available.
(d) It was useful for circles.

11. Who was the first of ancient philosophers to consider why geometric properties existed?
(a) Pythagoras.
(b) Thales.
(c) Hippocrates.
(d) Aristotle.

12. "Straight lines in the same plane that will never meet if extended forever" is a definition of what?
(a) Parallel lines.
(b) Circle.
(c) 180 degree angle.
(d) Intersection.

13. Which of the following is true in modern math about twin primes?
(a) They are not considered whole numbers.
(b) Their sum is always another prime number.
(c) We don't know if they are finite or infinite.
(d) They are infinite.

14. What is the name for determining the area of an enclosed space by constructing a square of equivalent area?
(a) Quadrature.
(b) Cubation.
(c) Triangulation.
(d) Square root.

15. Which words best describe how solid proofs were developed in Elements?
(a) Axiomatic framework.
(b) Programmed order.
(c) Simple arguments.
(d) Inverted scaffold.

Short Answer Questions

1. Which of the following becomes an important definition in mathematics that was first presented in Elements?

2. Who was the author of the book Elements?

3. What did Gauss set out to prove?

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

5. What did Apollonius work with in mathematics?

(see the answer keys)

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