PoW 1151

Seven Right Angles:  Barry Cox’s Movie

Data

soln1 = 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The Equations

Clear[a,b,c,d,e,f,g];
a={0,0,0};
b={1,0,0};
g={0,1,0};
c[A_]:={1, Cos@A, Sin@A};
f[CC_] :={Cos@CC, 1, Sin@CC};
d[A_,B_]:={1+Cos[B], Cos[A]-Sin[A]Sin[B], Sin[A]+Cos[A]Sin[B]};
e[CC_,DD_] :={Cos[CC]-Sin[CC]Sin[DD], 1+Cos[DD], Sin[CC]+Cos[CC]Sin[DD]};
Clear[hept];
hept[1]={a,b,c[#[[1]]],d[#[[1]], #[[2]]],e[#[[3]], #[[4]]],f[#[[3]]],g,a}& /@ soln1;
hept[2]={a,b,c[#[[1]]],d[#[[1]], #[[2]]],e[#[[3]], #[[4]]],f[#[[3]]],g,a}& /@ soln2;

The Animation

Manipulate[Graphics3D[{
If[hidecircle, {},{Red, Thick, Line[#[[3]]&/@ hept[k]]}],
{Red, Thick, Line[#[[6]]&/@ hept[k]];{}},
Thickness[.02], Tube[hept[k][[i]], .04]}, PlotRange-> {{-.9, 1.9},{-.9, 1.9},{-1.5, 1.5}}, 
ImageSize->600,PlotLabel->(If[k==1,soln1, soln2][[i,1]]; None)], {{k,2},{1,2}},{{i,1,"step"},1,Length[hept[k]],1, Appearance->"Open"}, {hidecircle, {False, True}}]

The A-graphs

aVals1 = First/@ soln1;
{Min[aVals1], Max[aVals1]}
aVals2 = First/@ soln2;
ListPlot[{aVals1, aVals2}]
{Min[aVals2], Max[aVals2]}