## Calculating Frenet triples in mathematica

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

aguacate
Posts: 209
Joined: Fri Feb 16, 2007 10:29 pm UTC

### Calculating Frenet triples in mathematica

Does anyone know if mathematica can calculate the curvature and torsion of a vector function? I would like to double check my geometry homework.

acidhak
Posts: 7
Joined: Sat Jan 26, 2008 6:15 pm UTC

### Re: Calculating Frenet triples in mathematica

I believe that this would require you to write modules first, i.e. there is no command to do this. If its for one time use, just compute from the definitions as things like gradient, dot product, cross product and norm are all very straight forward to use.

Here's one I had lying around for Gaussian curvature but I don't know if that helps you or not:

gaussK[x_][u_,v_] := Module[{xu,xv,xuu,xuv,xvv},

xu=D[x[uu,vv],uu]; xv=D[x[uu,vv],vv];

xuu=D[x[uu,vv],uu,uu];

xuv=D[x[uu,vv],uu,vv];

xvv=D[x[uu,vv],vv,vv];

Simplify[(Det[{xuu,xu,xv}]*Det[{xvv,xu,xv}]-Det[{xuv,xu,xv}]^2)/

(xu.xu*xv.xv-(xu.xv)^2)^2]]/.{uu->u,vv->v}

make it a .m file...

NathanielJ
Posts: 882
Joined: Sun Jan 13, 2008 9:04 pm UTC

### Re: Calculating Frenet triples in mathematica

I can't seem to find a pre-written mathematica module for things like torsion and curvature, but if you're able to use Maple instead then there are dozens of functions floating around the internet that will do it for you (even just a quick Google search pops up tons of them).
Homepage: http://www.njohnston.ca
Conway's Game of Life: http://www.conwaylife.com