Journey Through Genius: The Great Theorems of Mathematics Quiz | Four Week Quiz A

William Dunham (mathematician)
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This quiz consists of 5 multiple choice and 5 short answer questions through Archimedes' Determination of Circular Area.

Multiple Choice Questions

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

2. 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) That under Euclid's definition parallel lines can intersect.
(c) That angles in a triangles can not add up to more than 180 degrees.
(d) "Non-euclidean" geometry.

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

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

5. Which of the following is an example of a postulate that must be accepted in Elements?
(a) It is possible to draw an arc with any three points.
(b) It is possible to draw a straight line between an infinite number of points.
(c) It is possible to draw a circle that contains no lines.
(d) It is possible to connect any two points with a line and make a circle.

Short Answer Questions

1. Which was true of Euclid's number theory?

2. Which of Euclid's postulates troubled many of the following generations of mathematicians?

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

4. Which of the following was NOT true about Archimedes, according to Dunham?

5. Which of the following is an example of a perfect number?

(see the answer key)

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