Wednesday Answer


Solution: What is the smallest convex area in which a line segment of length 1 can be rotated 360 degrees? (A convex figure is one in which a straight line, joining any two of its points, lies entirely on the figure. Examples include circles and squares.)

Answer, an equilateral triangle of height 1. For the line segment to rotate, the sides have to be at least length 1. Of all convex figures with widths of 1, the equilateral triangle has the smallest area. Try taking a toothpick and a cardboard cutout of a triangle and check for yourself. To make it easier, glue a second toothpick in the middle of the first one to make an axle for rotating the first toothpick within the triangle cutout.

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