Journey Through Genius: The Great Theorems of Mathematics Quiz | Eight Week Quiz C

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

Multiple Choice Questions

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

2. What instruments did the Greeks use to square a shape?
(a) A sphere and ruler.
(b) A pendulum.
(c) A small grid.
(d) A compass and a ruled straight-edge.

3. According to Euclid, when is a triangle a right triangle?
(a) When a triangle can be constructed with three unequal sides.
(b) When a triangle does not have a side which can be considered a hypotenuse.
(c) When a triangle has three sides whose squares are equal to the area of the triangle.
(d) When a triangle has a side whose square is the sum of the squares of the two legs.

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

5. "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.

Short Answer Questions

1. Heron devised which of the following methods?

2. What range of values did Archimedes determine for pi?

3. When was the work of these early thinkers rediscovered again in history?

4. In general, what did Euclid's number theory describe?

5. In what century did Archimedes live?

(see the answer key)

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