Polygon Area - Polygon Net - dyn.Rotation homogene COS

Dynamic Rotation
Vertices={Vertices(1...n),Vertices(1)}[br][br]Matrix-Rotation Rn()[br][i]ROT={Rn(XVertices(j),YVertices(j),t_0)}[sub]j=1,n[/sub][/i][br][math]{\textcolor{brown}{o} Vertices \to Vertices_H\; _{roll}\to_{out}\; RVertices_H \to \textcolor{orange}{o} RVertices} [/math][br][math] \left\{\left(\prod_{i=1}^{j}ROT(i) \right) Vertices_H(j + 1)\right\}_{j=1...n}[/math][br][br]Rotation[i] by GeoGebra commands [br][br]n=6: [br]ROTi=Rotate[b]([/b][br] Rotate[b]([/b][br] Rotate[b]([/b][br] Rotate[b]([/b][br] Rotate[b]([/b][br] [color=#1155cc]Rotate(Element(Vertices, n+1), -t_0, Element(Vertices, n ))[/color],[br] -t_0, Element(Vertices, n - 1)[b])[/b],[br] -t_0, Element(Vertices, n - 2)[b])[/b], [br] -t_0, Element(Vertices, n - 3)[b])[/b], [br] -t_0, Element(Vertices, n - 4)[b])[/b],[br] -t_0,Element(Vertices,n - 5)[b])[br][br][sup][/sup][br][/b][i]ROTi[/i]=Iteration([br] Flatten({First(σ, Length(σ) - 2), {Rotate(Element(σ, Length(σ)), -t_0, Element(σ, Length(σ) - 1))}}), [br] σ, {Vertices}, n)[br][br]RVertices=Sequence([br]Iteration(Flatten({First(σ, Length(σ) - 2), {Rotate(Element(σ, Length(σ)), -t_0, Element(σ, Length(σ) - 1))}}), σ, {Take(Vertices, 1, k)}, k - 1), [br]k, n + 1, 1, -1)[br][/i][br]Sehr schöne spezielle Lösung nach [url=https://www.geogebra.org/u/mathmagic]Juan Vicente Sánchez[/url] [br]https://www.geogebra.org/m/jjdymhg5[br][br][i]IterationList(Rotate(Translate(σ, Vector(Element(σ, 3) - Element(σ, 2))), 360°/n - t_0, Element(σ, 3)), [br] σ, {[b]{M, Vertices(n), Vertices(1)}[/b]}, n - 1)[/i][br]

Information: Polygon Area - Polygon Net - dyn.Rotation homogene COS