Sattel

silviana amethyst

Equation ¶

Properties: ¶

• degree 3
• almost smooth, except for a point singularity at the origin
• unbounded

Some story ¶

I couldn’t tell from the image on Herwig Hauser’s gallery that this surface is not smooth. But it has that fun little pinch point! Bounded by a sphere of radius 1, with custom projection. For one parameterizing coordinate, we project onto \(x\) and \(y\). The other is onto \(z\).

Bertini_real input files ¶

input

CONFIG
tracktype: 1;
sharpendigits: 20;
randomseed: 1;
finaltol: 1e-14;
endgamenum: 2;
numsamplepoints: 4;
END;
INPUT

variable_group x, y, z;
function f;
f = x^2+y^2*z+z^3;
END;