6.BK SUPERELLIPSE
New section.
Gardner. SA (Sep 1965) = Carnival, chap. 18. Describes how the problem arose in the design of Sergel's Square, Stockholm, in 1959. Addendum in Carnival gives the results given by Gridgeman, below. Also says road engineers used such curves with n = 2.2, called '2.2 ellipses', from the 1930s for bridge arches.
N. T. Gridgeman. Lamé ovals. MG 54 (No. 387) (Feb 1970) 31 37. Lamé (c1818) seems to be the first to consider (x/a)n + (y/b)n = 1. Hein's design in Stockholm uses a/b = 6/5 and n = 5/2. Gerald Robinson used a/b = 9/7 and n = 2.71828..., which he determined by a survey asking people which shape they liked most. Gridgeman studies curvature, area, perimeter, evolutes, etc.
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