Gebruiker:Martinvl/Fibonaccireeks: Verskil tussen weergawes

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Martinvl (besprekings | bydraes)
Martinvl (besprekings | bydraes)
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=== Sferiese spirale ===
 
Die oppervlak van 'n sfeer, radius <math>r</math>, kan voorgestel word deur die volgende vergelykings:[https://<ref>{{cite web
|url = mathcurve.com/courbes3d.gb/clelie/clelie.shtml citation]
|title = Clelia
 
|first1 = Robert
: <math>
|last1 = Ferréol
|first2 = Jacques
|last2 = Mandonnet
|publisher = mathcurve.com
|year = 2018
|language = English}}</ref>
[https://mathcurve.com/courbes3d.gb/clelie/clelie.shtml citation]: <math>
\begin{array}{cll}
x &=& r \cdot \sin \theta \cdot \cos \varphi \\
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</math>
 
andWaneer sets<math>\varphi</math> voorgestel is thedeur lineardie dependencyvergelyking <math>\; \varphi=c\theta , \; c> 2\; ,</math>, forkry the'n anglemens coordinates, one'n getssferiese akurwe [[sphericalmet curve]]die callednaam '''sphericalsferiese spiralspiraal'''. <ref>Kuno Fladt: ''Analytische Geometrie spezieller Flächen und Raumkurven'', Springer-Verlag, 2013, {{ISBN|3322853659}}, 9783322853653, S. 132</ref> withmet thedie parametricparametriese representationvoorstelling (with <math>c</math> equalis togelyk twiceaan thetwee numberkeer ofdie turnsaantal draaie):
* <math>
\begin{array}{cll}
x &=& r \cdot \sin \theta \cdot \cos{\color{red} c\theta} \\
y &=& r \cdot \sin \theta \cdot \sin {\color{red}c\theta} \\
z &=& r \cdot \cos \theta\qquad \qquad 0\le\theta\le \pi \ .
\end{array}