But we are not talking about finding maxima and minima of real-valued
functions, because the general funciotn-surface is a level surface of a
function of three variables. So, deriving a sphere function, x*x+y*y+z*z-1,
gives you a 3-vector (gradient): grad f = <2x. 2y, 2x>. Solving this for
zero as you would with normal functions yields <0, 0, 0>, which means that
the function has a extreme point at <0, 0, 0> In fact, it's a minimum, but
this is at the centre of the sphere, which is _not_ the lowes point on the
sphere. (Of course not, I'd say.) This minimum represents the 'density' of a
4-d-object, and the sphere itself is the set of all denisties with a
specific value, for example r^2.

It would be lesser problems if one were able to solve the function for for
example y by saying:

x*x+y*y+z*z=1 => y = +-sqrt(1-x*x-z*z) and this function we can derive and
find maxima and minima of. BUT NOT from for example: sin x - x = 0, which
have noe algebraic solutions!

Warp skrev i meldingen <38db2db8@news.povray.org>...
>  If I remember right, you can calculate minimums and maximums by deriving
>the function twice. So there wouldn't be any problem.
>
>--
>main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
>):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/

Post a reply to this message