Envelopes and String Art

Author: Quenell Gregory  

Publisher: Mathematical Association of America

ISSN: 1930-0980

Source: Mathematics Magazine, Vol.82, Iss.3, 2009-06, pp. : 174-185

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Abstract

The base of a ladder is being pulled away from a wall at a constant rate. In a stroboscopic photograph of this act, the ladder would show up as a family of line segments whose upper edge approximates a curve, which is called their envelope. We discuss an elementary way to identify the envelope of a family of line segments, and consider several examples involving ladders, game theory, and nails driven into a board and connected by strings.