Wolfram Cloud Document

Poncelet triangles and the amazing loci of the isogonal conjugates
by Dan Reznik

Inspired by a 2013 by A. Skutin (see below), I am using Mathematica to investigate the locus of the isogonal conjugate of a fixed point P wrt to a family of Poncelet triangles.
I have made two videos to illustrate all the curious observations:

paper: [1] A. Skutin, “On Rotation of a Isogonal Point”, Journal of Classical Geometry, vol. 2, 2013. https://jcgeometry.org/Articles/Volume2/JCG2013V2pp66-67.pdf

Load files

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Get["equalAxesCpRectBoth.m"];Get["isogEnvConfocal.m"];

Initialization Code
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(prepare manip) Locus of Isogonal conjug. of fixed point
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(main manip app) Locus of Isogonal conj. of fixed point

(*Clear@equalAxesCpRectBoth;Clear@isogEnvConfocal;Get["data/equalAxesCpRectBoth.m"];Get["data/isogEnvConfocal.m"];*)

In[]:=

Manipulate[Show[showIsogIsotLocus[getPreset["n=3 non-conc tilt A"],tDeg,{px,py},extras(Join[If[drConicDelims,List@@equalAxesCpRectBoth,{}],If[drIsogEnv,List@@isogEnvConfocal,{}]]),cevXk0,locusSteplocusStep0,maxDistmaxDist0,scalescale0,txtx0,tyty0,pDegpDeg0,wherePwhereP0,debugFalse,drTrisFalse,drIsogsdrIsogs0],PlotRange{{-2,2},{-2,2}}],{{px,.3},-2,2,.01},{{py,-.2},-2,2,.01},{{whereP0,"none"},{"none","inner","outer"}},{{tDeg,20.},-360,360,1},{{pDeg0,30.},-360,360,1},Delimiter,{{drIsogs0,True,"locus isog"},{True,False}},(*{{drIsots0,False,"locus isot"},{True,False}},*){{drConicDelims,False,"isog conic delims"},{True,False}},{{drIsogEnv,False,"isog envelope"},{True,False}},Delimiter,(*{{cevType0,"none","cev type"},{"none","cevian","anticevian","pedal","antipedal","reflection"},PopupMenu},{{cevXk0,0,"cevian

"},0,1000,1},{{drCevCircum0,False,"cev.circum."},{True,False}},*){{locusStep0,2.5,"locus step"},{.1,.25,.5,1,2.5,5,10}},{{maxDist0,10,"maxDist"},{5,10,25,50,100}},Delimiter,{{scale0,1},.1,2,.01},{{tx0,0},-2,2,.1},{{ty0,0},-2,2,.1},ControlPlacementRight,SaveDefinitionsTrue]

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