Thales theorem illustrated with manipulation
Sándor Kabai
MathWord: An inscribed angle in a semicircle is a right angle.
Thales’s theorem is illustrated here with a reverse triangle and a cube to emphasise the perpendicularity.
MathWord: An inscribed angle in a semicircle is a right angle.
Thales’s theorem is illustrated here with a reverse triangle and a cube to emphasise the perpendicularity.
In[]:=
Manipulate[cir=ParametricPlot3D[{Sin[x],Cos[x],0},{x,0,2Pi},PlotStyle->{Yellow,Tube[0.01]}][[1]];spA=Sphere[{-1,0,0},0.03];spB=Sphere[{1,0,0},0.03];spC=Sphere[{-Cos[alf],Sin[alf],0},0.03];spD=Sphere[{Cos[alf],-Sin[alf],0},0.03];dia=Cylinder[{{-1,0,0},{1,0,0}},0.02];line1=Cylinder[{{-1,0,0},{-Cos[alf],Sin[alf],0}},0.02];line2=Cylinder[{{1,0,0},{-Cos[alf],Sin[alf],0}},0.02];pol1=Polygon[{{-1,0,0},{1,0,0},{-Cos[alf],Sin[alf],0}}];pol2=Polygon[{{-1,0,0},{1,0,0},{Cos[alf],-Sin[alf],0}}];dia1=Line[{{-Cos[alf],Sin[alf],0},{Cos[alf],-Sin[alf],0}}];cub=PolyhedronData["Cube","Faces"];cubn=Translate[Rotate[Translate[Scale[cub,0.5{1,1,1},{0,0,0}],{0.25,-0.25,0}],alf/2,{0,0,1}],{{-1,0,0}}];cubt=Rotate[cubn,-alf,{0,0,1}];Graphics3D[{line2,line1,dia1,spD,LightGreen,pol2,Cyan,pol1,Red,spC,Green,dia,Purple,spB,spA,cir,Pink,cubt},Boxed->False,SphericalRegion->True,ViewPoint->{0,100,100},PlotRange->1.1,ViewAngle->0.008],{{alf,Pi/2,"angle"},0,Pi},TrackedSymbols:>alf]
Out[]=
