Calvin and Hobbes by Bill Watterson for April 27, 1987
April 26, 1987
April 28, 1987
Transcript:
Book: Point A is twice as far from point C as point B is from A. If the distance from point B to point C is 5 inches, how far is point A from point C? Calvin: The living dead don't need to solve word problems.
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The lengths of the sides are X, 2X, and 5. We are asked to find 2X. The term “distance” is used, so the triangle inequality applies. Therefore:
X + 2X >= 5
X + 5 >= 2X
5 + 2X >= X
Reducing, and solving for 2X:
2X >= 3 1/3
2X <= 10
2X >= -10
So all we know, without further assumptions is that AC is between 3 1/3 and 10, inclusive.
Note that this analysis does not assume and particular distance function. In particular it does not assume a distance function derived from a euclidian norm. But I doubt Calvin’s teacher could even tell you what that means.