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. In what century did Archimedes live?
(a) First century A.D,
(b) Twelthf century A.D.
(c) Third century B.C.
(d) Nineteeth century A.D.

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

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

4. Which of the following is true about pi, as described by Dunham.
(a) The measurement of pi was redetermined after Archimedes's death.
(b) The measurement of pi should not have been so difficult for Archimedes to demonstrate.
(c) The measurement of pi is no longer a mystery as we have an exact number value in modern mathematics.
(d) The measurement of pi is a challenge that continues into modern mathematics.

5. Where did Hippocrates come from?
(a) Rome.
(b) Athens.
(c) Chios.
(d) Constinople.

6. Where was Neil's Abel from?
(a) Ireland.
(b) Finland.
(c) Great Britian,
(d) Norway.

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

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

9. What did Dunham discuss for many pages in this chapter?
(a) Heron's political tendancy.
(b) Heron's religious beliefs-
(c) Heron's origins of the universe.
(d) Heron's complicated proof.

10. How did Archimedes demonstrate his theory of pi?
(a) He demonstrated that the area of the circle is never equal to the area of the triangle.
(b) He demonstrated that the area of the circle is always greater than the area of the triangle.
(c) He demonstrated that the area of the circle is never less than the area of the triangle.
(d) He demonstrated that the area of the circle is neither greater than nor less than the area of the triangle and therefore must be equal to it.

11. Which of the following was an important proposition given by Euclid's number theory?
(a) Any even number is divisible by 3.
(b) Numbers from one to ten are only divisible by composite numbers.
(c) Any perfect number is divisible by some composite number.
(d) Any composite number is divisible by some prime number.

12. 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.

13. In what time period did mathematicians find a solution to cubic equations?
(a) Seventeeth century.
(b) Twentieth century.
(c) Fifteen century.
(d) Thirteenth century.

14. What did Hippocrates do that advanced mathematical methods?
(a) He created a new ways to disprove theories.
(b) He proved that mathematics can be applied in a unlogical order.
(c) He demonstrated that geometry does not have to be based on previous knowledge.
(d) He built theorems based on sequencially more complex proofs.

15. Which of the following was NOT one of Gauss' discoveries?
(a) That angles in a triangles can not add up to more than 180 degrees.
(b) That under Euclid's definition parallel lines can intersect.
(c) "Non-euclidean" geometry.
(d) That there is no apparent contraction to the assumption that the sum of angles in a triangle can have fewer than 180 degrees.

Short Answer Questions

1. What was Hippocrates famous for?

2. What else, besides a solution to cubic equations, was in Cardano's book?

3. Which is one of the common notions presented in Elements?

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

5. As described by Archimedes, what is always true about he diameter of the circle?

(see the answer keys)

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