Shattering the Plane with Twelve New Substitution Tilings Using 2, φ, ψ, χ, ρ
Similar Triangle Dissections
Version 12 of the Wolfram Language introduces solvers for geometry problems. The documentation for the new function GeometricScene has a neat example showing the following piece of code, with GeometricAssertion calling for seven similar triangles: [Wolfram_Notebook_Download]
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o=Sequence[Opacity[.9],EdgeForm[Black]];plasticDissection=RandomInstance[GeometricScene[{a,b,c,d,e,f,g},{
a=={1,0},e=={0,0},Line[{a,e,d,c}],
p0==Polygon[{a,b,c}],
p1==Style[Polygon[{b,d,c}],Orange,o],
p2==Style[Polygon[{d,f,e}],Yellow,o],
p3==Style[Polygon[{b,f,d}],Blue,o],
p4==Style[Polygon[{g,f,b}],Green,o],
p5==Style[Polygon[{e,g,f}],Magenta,o],
p6==Style[Polygon[{a,e,g}],Purple,o],
GeometricAssertion[{p0,p1,p2,p3,p4,p5,p6},"Similar"]}],RandomSeeding->28]
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