Steven Dutch, Natural and Applied Sciences, University
of Wisconsin - Green Bay

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Is there anyone who never did this with graph paper in school? Number the squares from, say, 1 to 10 along the x- and y- axes. Connect 1 and 9, 2 and 8, and so on, always keeping the sum of the intercepts equal to some constant, in this case 10. You get a graceful curve.

Actually, the curve is a parabola, and that can be easily seen if you go into
negative numbers, connecting 11 and -1 and so on, and extending the lines. The
equation of the parabola is x^{1/2} + y^{1/2} = 1. In standard
form it becomes the less elegant x^{2} + y^{2}
-2xy -2x -2y +1 = 0. The xy term is the giveaway that the axis is tilted, and
the x and y terms show that the origin is not at the vertex.

Sum of Intercepts (pixels): Interval between lines (Pixels):

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*Created 18 January 2008, Last Update
17 December 2010
*

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