calcolo integrale, Peano had already provided different correct conditions for a function to attain a local minimum or local maximum. In the 1899 German translation of the same textbook, he provided this surface as a counterexample to Serret's condition. At the point , Serret's conditions are met, but this point is a saddle point, not a local maximum. A related condition to Serret's was also criticized by Ludwig Scheeffer, who used Peano's surface as a counterexample to it in an 1890 publication, credited to Peano. Models Models of Peano's surface are included in the Göttingen Collection of Mathematical Models and Instruments at the University of Göttingen, and in the mathematical model collection of TU Dresden (in two different models). The Göttingen model was the first new model added to the collection after World War I, and one of the last added to the collection overall. References External links Differential geometry of surfaces Algebraic surfaces