Peano surface

In mathematics, the Peano surface is the graph of the two-variable function

${\displaystyle f(x,y)=(2x^{2}-y)(y-x^{2}).}$

It was proposed by Giuseppe Peano in 1899 as a counterexample to a conjectured criterion for the existence of maxima and minima of functions of two variables.

The surface was named the Peano surface (German: Peanosche Fläche) by Georg Scheffers in his 1920 book Lehrbuch der darstellenden Geometrie. It has also been called the Peano saddle.