and so for a given lambda x=y=z.
Replace y and z with x and you get
Trying to solve with x, y, and z being maybe different makes the algebra horrible but as they are equal it's enough to solve 3x^4 = 1 which you have done.
Bob
]]>Your point hits the shape :-)
How have you gotten 3*x^4=1 ?
I moved everything to one side:
x^4+y^4+z^4-1=0
f*x+f*y+f*z-r=0
Set them equal:
x^4+y^4+z^4-1=f*x+f*y+f*z-r
And tried to solve the above for x,
but this gave me wild formulas.
It looks like you've got
The line joining the origin to (1,1,1) is
So every point on the line has x = y = z
So it will intersect the shape at
Hope that helps,
Bob
]]>I tried it with y=x+z and y=3-x-z,
but the computer says I'm giving planes.
Is it possible to somehow get the point, where they intersect ?
For numericals, one could take a=1 and n=4.
Edit: Being unsure what the correct equation for the line is.
]]>