[This site of the late Ron Resch was restored by Mitya Miller from the web fetch copy provided by Erik Demaine, with permission from his son Yon Resch and guidance provided by Robert J. Lang. If you spot any missing or broken links or images, please report them.]
Resch Curve (Folded) — Ron Resch Official Website
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Resch Curve (Folded)

These shaded computer images are really the precursor to my discovery of the Resch Curve in which there are two curves in two plane squares at right angles and edge connected (see below: diagram, and math paper link ). In this study one "curve" is a straight line, and the other is a quarter circle arc. The points of these curves are also the respective end points of a family of unit distance lines. Each line is constant in its' Z value.

Resch Curve_Fig_Zig-Zag_Page_02.CROP
Resch Pre-Curve-Diagram-6
RonReschCurve_08
RonReschCurve_05.Crop
RonResch02_01
RonResch02_02.Crop
RonResch02_04.Crop
RonResch03_01
RonResch03_02.Crop