[size=85][size=50][right][i][b][size=50]Diese Aktivität ist eine Seite des [color=#980000]geogebra-books[/color] [url=https://www.geogebra.org/m/xtueknna][color=#0000ff][u]geometry of some complex functions[/u][/color][/url] [color=#ff7700]october 2021[/color][/size][/b][/i][/right][/size][br][color=#cc0000][u][i][b]Zitat[/b][/i][/u][/color]:[color=#0000ff][u][i][b] [url=https://en.wikipedia.org/wiki/M%C3%B6bius_transformation]wikipedia[/url][/b][/i][/u][/color][br][math]\approx[/math] "Given a set of three distinct points [b]z[sub]1[/sub][/b], [b]z[sub]2[/sub][/b], [b]z[sub]3[/sub][/b] in [math]\mathbb{C}\cup \{ \infty\}[/math] and a second set of distinct points [b]w[sub]1[/sub][/b], [b]w[sub]2[/sub][/b], [b]w[sub]3[/sub][/b], [br]there exists precisely [i][b]one[/b][/i] Möbiustransformation [b]T(z)[/b] with [b]T(z[sub]i[/sub])[/b] = [b]w[sub]i[/sub][/b] for [b]i[/b] = 1,2,3." [br][br][color=#cc0000][i][b]For example:[/b][/i][/color] [b]0[/b], [b]1[/b], [math]\mathbf{\infty}[/math] ---> [b]T[/b] ---> [b]w[sub]0[/sub][/b], [b]w[sub]1[/sub][/b], [b]w[/b][math]\mathbf{_{\infty}}[/math]; [br] [math]\mathbf{T}\left(z\right):=\frac{\left(w_1-w_0\right)\cdot w_{\infty}\cdot z-\left(w_1-w_{\infty}\right)\cdot w_0}{\left(w_1-w_0\right)\cdot z-\left(w_1-w_{\infty}\right)}[/math].[br][br] If w[math]_{\infty}[/math]=[math]\infty[/math], [math]\mathbf{T}\left(z\right):=\left(w_1-w_0\right)\cdot z+w_0[/math][/size]