Joel C. Langer and David A. Singer, The lemniscatic chessboard,
Forum Geometricorum, 11 (2011) 183--199.
Abstract.
Unit speed parametrization of the lemniscate of Bernoulli is given by a simple
rational expression in the lemniscatic sine function. The beautiful
structure of this parametrization becomes fully visible only when complex values
of the arclength parameter are allowed and the lemniscate is viewed
as a complex curve. To visualize such hidden structure, we will
show squares turned to spheres, chessboards to lemniscatic
chessboards.
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