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We consider how a standard theorem in algebraic geometry relating properties of a curve with a (Z/2Z)²-action to the properties of its quotients generalizes to results about sets and graphs that admit (Z/2Z)²-actions. [ABSTRACT FROM AUTHOR]

This article presents a study regarding multivariate calculus, focusing on saddle points and inflection points. It discusses the similarities between saddle points on surfaces and inflection points on curves. It explores the direct connection between saddle points on surfaces and inflection points on curves. It presents the theorem which provides a simple constructive method to obtain continuous functions to connect the saddle points of functions of two variables with the inflection points of functions of one variable.

The article discusses the mathematical principles and applications concerning the families of plane algebraic curves that contain a special set of points. The case of curves in cages is associated with the elementary methods that presume the familiarity with algebraic geometry and geometrical applications. These applications can be considered as natural generalizations of classical theorems in projective geometry and are associated with familiarity with Pascal's theorem and its comparison with the classical Pascal diagram.