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

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

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

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

5. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?
(a) Since the circumference can also be expressed as twice the radius multiplied by π, the area is 2πr²/2, or πr².
(b) The area of a triangle is one half the base times the height.
(c) Since the diameter of a circle is equal to the hypotenuse of the right triangle, the area of the triangle in his proof is 1/2 the radius times the circumference.
(d) Since the base of the triangle is equal to the circumference and the height is the radius, the area of the triangle in his proof is 1/2 the radius times the circumference.

6. 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.

7. Heron's work referred to the work of what other famous scholar?
(a) Hippocrates.
(b) Euclid.
(c) Archimedes.
(d) Thales.

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

9. 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,

10. Who was Heron?
(a) A philosopher from Greece.
(b) A politician from Rome.
(c) A physician from the far East.
(d) A matematician from Alexanderia.

11. What range of values did Archimedes determine for pi?
(a) Between 3 1/2 and 3 5/8.
(b) Between 3 10/11 and 3 1/7.
(c) Between 3 and 3 1/2.
(d) Between 3 and 4.

12. 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.

13. 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.

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

15. What did Heron's advances put into historical perspective for Dunham?
(a) A shift in information flow that ignored socioeconomic order.
(b) A shift in learning across continents.
(c) A change in learning foundations in the ancient scholarly universities.
(d) A change in political theory across the globe.

Short Answer Questions

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

2. Which of the following is false about the modern implications of Euclid's number theory?

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

4. Who acted as the gate keepers of knowledge?

5. Which of the following was an important proposition given by Euclid's number theory?

(see the answer keys)

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