Gebruiker:Martinvl/Fibonaccireeks: Verskil tussen weergawes

:<math>x=r(\varphitheta)\cos\varphitheta \ ,\qquad y=r(\varphitheta)\sin\varphitheta</math>

is given, then there can be added a third coordinate <math>z(\varphitheta)</math>, such that the now space curve lies on the [[cone]] with equation <math>\;m(x^2+y^2)=(z-z_0)^2\ ,\ m>0\;</math>:

* <math>x=r(\varphitheta)\cos\varphitheta \ ,\qquad y=r(\varphitheta)\sin\varphitheta\ , \qquad \color{red}{z=z_0 + mr(\varphitheta)} \ .</math>

Starting with an ''archimedean spiral'' <math>\;r(\varphitheta)=a\varphitheta\;</math> one gets the conical spiral (see diagram)

:<math>x=a\varphitheta\cos\varphitheta \ ,\qquad y=a\varphitheta\sin\varphitheta\ , \qquad z=z_0 + ma\varphitheta \ ,\quad \varphitheta \ge 0 \ .</math>