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A program initiated by F. Klein in an 1872 lecture to describe geometric structures in terms of their automorphism groups.

A catastrophe which can occur for one control factor and one behavior axis. It is the universal unfolding of the singularity f(x)=x^3 and has the equation F(x,u)=x^3+ux.

The H-fractal is a fractal constructed by starting with the line segments corresponding to a capital letter H, then iteratively placing smaller H's centered at the top and ...

A metric on a bunch of segments with a common endpoint O, which defines the distance between two points P_1 and P_2 as the length of the shortest path connecting them inside ...

A homology class in a singular homology theory is represented by a finite linear combination of geometric subobjects with zero boundary. Such a linear combination is ...

A catastrophe which can occur for three control factors and two behavior axes. The hyperbolic umbilic is the universal unfolding of the function germ f(x,y)=x^3+y^3. The ...

The term "ice fractal" refers to a fractal (square, triangle, etc.) that is based on a simple generating motif. The above plots show the ice triangle, antitriangle, square, ...

The interior of a set is the union of all its open subsets. More informally, the interior of geometric structure is that portion of a region lying "inside" a specified ...

The isogonal transform of a geometric object is the object obtained by collectively taking the isogonal conjugates of all its points.

Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or ...