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

2. 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 neither greater than nor less than the area of the triangle and therefore must be equal to it.
(c) He demonstrated that the area of the circle is always greater than the area of the triangle.
(d) He demonstrated that the area of the circle is never less than the area of the triangle.

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

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

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

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

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

8. According to Dunham, who was most able to collect knowledge from around the globe?
(a) Greek philosophers.
(b) Greek tradesman.
(c) Roman emporers.
(d) Arabian scholars.

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

10. Which of the following best describes Cardano's character?
(a) Eccentric.
(b) Flirtacious.
(c) Arrogant.
(d) Religious.

11. Which of the following becomes an important definition in mathematics that was first presented in Elements?
(a) Parallel line.
(b) Intersection.
(c) 180 degree angle.
(d) Circle.

12. Who wrote a treatise that supposed that cubic equations may be impossible to solve?
(a) Scipione del Ferro.
(b) Luca Pacioli.
(c) Niccolo Fontana.
(d) Gerolamo Cardano.

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

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

15. What did Dunham consider extraordinary about the Elements?
(a) The content was totally unique.
(b) The content was not based on previous authors' work.
(c) How Hippocrates ordered the book.
(d) How geometric proofs were presented.

Short Answer Questions

1. Which of the following is INCORRECT, and not used in Archimedes proof of his theory?

2. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?

3. Who asked Tartaglia for his solution to cubic equations?

4. Which of the following was true about Cardano, according to Dunham?

5. How many definitions were stated in Elements?

(see the answer keys)

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