Architect and engineer . ts upperreaches, presages the conchoidal character-istic of reversing its curvature. Finally,between the plump parabola as one limit,and the straight line as the other, an in-finite number of hyperbolas exist havingthe same limiting pair of rectangular co-ordinates. It is conceivable that one ofthese innumerable hyperbolas might be ac-ceptable as an entasis curve. But try andfind it! Wherefore, once upon a time . . butthis is no fable ... I set myself the taskof inventing an entasis curve that wouldsatisfy not only the aesthetic requirementsof the case but likewise the
Architect and engineer . ts upperreaches, presages the conchoidal character-istic of reversing its curvature. Finally,between the plump parabola as one limit,and the straight line as the other, an in-finite number of hyperbolas exist havingthe same limiting pair of rectangular co-ordinates. It is conceivable that one ofthese innumerable hyperbolas might be ac-ceptable as an entasis curve. But try andfind it! Wherefore, once upon a time . . butthis is no fable ... I set myself the taskof inventing an entasis curve that wouldsatisfy not only the aesthetic requirementsof the case but likewise the practical de-mand for a simple and direct method offull-size detailing. To meet the latter de-mand, the sought-for curve must yield toscaled-down vertical compression whilst,at the same time, maintaining its horizontalordinates [all size. The drawing herewith records the netresults of my investigations. You will notethat I have invented not onlv one. but an JHt rANOID .AND 1T5 APPLICATION TOTHL DETAILING or. DLTAIL GgAPH OP tNTA5l5 VL^TICAL 3CALL, yz= I-OHORIZONTAL 5CALL, TULL 3IZE ^PI-LL tVATIONAT V5(;?VLL -f^+^ <^ DETAIL GRAPH OF ENTASISErnest I. Freese, Architect entire family of subtle mathematical curveshaving the required properties. I havenamed these new curves fanoids; a sim-ple designation based on their collectiveappearance as shown at Diagram 1. Thegeneration of a fanoidal curve is startlingly free from geometric intricacy. At Dia-gram 1, let AA be a fixed circle, and BB afixed straight line; and let any number ofcircles be drawn tangent to AA and cen-tered on BB. Whence, homologous pointsof the variable circles are the generating THE ARCHITECT AND ENGINEER ^ 22 ? JANUARY, NINETEEN THIRTY-FOUR points of the fanoidal family tree, as simplest fanoid is the one whose gen-erating point is one end of the diameterthat lies square with BB. Moreover, thisparticular fanoid becomes a direct graph ofthe sought-for entasis curve, when the ver-tical ordinates of the
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