Harmonische Lage

[table][tr][td][url=https://www.geogebra.org/m/y9cj4aqt#material/nhnwaakc][img]data:image/png;base64,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[/img][/url][/td][td] [size=50]Diese Aktivität ist eine Seite des [color=#980000][b]geogebra-books[/b][/color] [br] [url=https://www.geogebra.org/m/nzfg796n][color=#0000ff][u][b]Elliptische Funktionen & Bizirkulare Quartiken & ...[/b][/u][/color][/url] ([color=#ff7700][i][b]05.02.2023[/b][/i][/color])[/size][/td][/tr][/table]
[right][size=85][size=50][size=50][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]Dezember 2021[br][/color][/size][/b][/i][/size]Diese Aktivität ist auch eine Seite des [color=#980000][i][b]geogebra-books[/b][/i][/color] [url=https://www.geogebra.org/m/fzq79drp][u][color=#0000ff][i][b]Leitlinien und Brennpunkte[/b][/i][/color][/u][/url] ([color=#ff7700][i][b]September 2021[/b][/i][/color])[/size][/size][size=85][br][/size][/right][size=85]Ist die [i][b]absolute Invariante[/b][/i] der vier [u][i]verschiedenen[/i][/u] [color=#00ff00][i][b]Brennpunkte[/b][/i][/color] gleich Null, so besitzen die [color=#00ff00][i][b]Brennpunkte[/b][/i][/color] [color=#0000ff][i][b]harmonische Lage[/b][/i][/color] [br]und umgekehrt.[br]Die [color=#00ff00][i][b]Brennpunkte[/b][/i][/color] liegen dann sowohl auf einem [color=#ff0000][i][b]Kreis[/b][/i][/color] als auch spiegelbildlich auf zwei orthogonalen [color=#ff0000][i][b]Kreisen[/b][/i][/color].[br]In [color=#0000ff][i][b]Normalform[/b][/i][/color] sind [math]f=e^{\frac{\pi}{4}\cdot i},f'=-e^{\frac{\pi}{4}\cdot i},f''=e^{\frac{-\pi}{4}\cdot i},f'''=-e^{\frac{-\pi}{4}\cdot i}[/math] die [color=#00ff00][i][b]Brennpunkte[/b][/i][/color] und damit [br]die [color=#9900ff][i][b]Nullstellen[/b][/i][/color] der zugehörigen [color=#9900ff][i][b]elliptischen Differentialgleichung[/b][/i][/color]:[br][/size][list][*][math]\left(g'\right)^2=c\cdot\left(g-f\right)\cdot\left(g+f\right)\cdot\left(g-\frac{1}{f}\right)\cdot\left(g+\frac{1}{f}\right)\mbox{ mit } c\in\mathbb{C}[/math], [size=85]wegen[/size] [math]f^2=i[/math] [size=85]ergibt das [/size][math]f^2+\frac{1}{f^2}=0[/math][/*][*][size=85]und damit die Differentialgleichung[/size] [math]\left(g'\right)^2=c\cdot\left(g^4+1\right)[/math][br][/*][/list][size=85][color=#ff7700][color=#000000]Geschlossene [/color][i][b]Lösungskurven[/b][/i][/color] sind dann [color=#38761D][i][b]konfokale[/b][/i][/color] 2-teilige [color=#ff7700][i][b]bizirkulare Quartiken[/b][/i][/color],[br]und im 45°-Winkel dazu 1-teilige [color=#ff7700][i][b]bizirkulare Quartiken[/b][/i][/color]![br]Im Applet oben wird aus jeder diese Scharen eine [color=#ff7700][i][b]bizirkulare Quarti[/b][/i][/color]k angezeigt, durch Bewegen von [color=#20124D][b]q[/b][/color] oder [br]der [color=#cc0000][i][b]Scheitelpunkte[/b][/i][/color] [color=#cc0000][b]s[/b][/color] erhält man andere Lagen. [br]Jede dieser Scharen enthält [color=#0000ff][i][b]möbiusgeometrisch[/b][/i][/color] genau eine [b]CASSINI[/b]-Quartik. [br]Für diese liegt der [color=#900000][i][b]Spiegelpunkt[/b][/i][/color] [color=#980000][b]f#[/b][/color] von [color=#00ff00][b]f[/b][/color], gespiegelt an dem [color=#0000ff][i][b]Leitkreis[/b][/i][/color], auf einem der Punkte [math]0,1,i,-i,-1,\infty[/math]; [br]falls [color=#980000][b]f#[/b][/color] auf [math]\infty[/math] zu liegen kommt, ist [color=#00ff00][b]f[/b][/color] Mittelpunkt des [color=#0000ff][i][b]Leitkreises[/b][/i][/color].[br][/size]
[br][table][tr][td][size=85]Wäre die zur obigen [color=#9900ff][i][b]elliptischen Differentialgleichung[/b][/i][/color] [br]gehörende [color=#38761D][i][b]elliptische Funktion[/b][/i][/color] in [color=#980000][i][b]ge[icon]https://www.geogebra.org/images/ggb/toolbar/mode_sphere2.png[/icon]gebra[/b][/i][/color] [br]implementiert, so könnte man die [color=#ff7700][i][b]bizirkularen [br]Lösungskurven[/b][/i][/color] einfach mit Hilfe eines quadratischen [color=#7F6000][i][b][br]Gittergewebes[/b][/i][/color] mit Diagonalen darstellen[/size].[/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table]
links
[size=50][size=50][color=#cc0000][i][b]geogebra-book[/b][/i][/color] [/size][b][size=50][color=#0000ff][b]Möbiusebene[/b][/color][/size][/b] [/size][size=50]Kap.: [color=#351C75][u][b][url=https://www.geogebra.org/m/kCxvMbHb#chapter/168947]Lage von 4 Punkten[/url][/b][/u][/color][br][/size][size=50][color=#cc0000][i][b]geogebra-book[/b][/i][/color] [color=#0000ff][b]Möbiusebene[/b][/color] Kap.:[color=#351C75][b] [url=https://www.geogebra.org/m/kCxvMbHb#chapter/168952]Quadratische Vektorfelder oder elliptische Funktionen[br][/url][/b][/color][color=#cc0000][i][b]geogebra-book:[/b][/i][/color] [color=#0000ff][b]conics bicircular-quartics Darboux-cyclides[/b][/color] Kap.: [url=https://www.geogebra.org/m/gz4cyje5#chapter/603410][color=#351C75][b][u]elliptic functions[/u][/b][/color][/url][br][/size][size=50][size=50][color=#cc0000][i][b]geogebra-book:[/b][/i][/color][/size]: [url=https://www.geogebra.org/m/fzq79drp][u][color=#20124D][b]Leitlinien und Brennpunkte (foci and directrices)[/b][/color][/u][/url][/size]

Information: Harmonische Lage