Re: Plotting the Lemniscate of Bernoulli
- To: mathgroup at smc.vnet.net
- Subject: [mg59889] Re: Plotting the Lemniscate of Bernoulli
- From: "Narasimham" <mathma18 at hotmail.com>
- Date: Wed, 24 Aug 2005 06:32:49 -0400 (EDT)
- References: <de6mda$cjk$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
The Lemniscate of Bernoulli is a planar curve. So you want a twisted
toroidal tube with either t or u varied such that it is a Lemniscate
of Bernoulli by displacement or rotation? These are planar sections
with zero torsion.
Rotation of the Lemniscate around y - axis produces a zero hole
toroidal surface of revolution, but it may not be very interesting.
Quite apart from that, this one works.(Changes in Pi and PlotPoints).
knot1 = ParametricPlot3D[{2*(10 + Cos[u])(Cos[t])/(1 + Sin[t]^2),
(10 + Sin[u])(Sin[t]Cos[t])/(1 + Sin[t]^2),u*Sin[t]},{t, 0,2*Pi },
{u, 0,3}, PlotPoints -> {65,5}, ViewPoint -> {1, 2, 1}] ;