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The geometry resulting from the application of the inversion operation. It can be especially powerful for solving apparently difficult problems such as Steiner's porism and ...

The study of manifolds having a complete Riemannian metric. Riemannian geometry is a general space based on the line element ds=F(x^1,...,x^n;dx^1,...,dx^n), with F(x,y)>0 ...

That portion of geometry dealing with figures in a plane, as opposed to solid geometry. Plane geometry deals with the circle, line, polygon, etc.

The branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called "higher ...

Triangle geometry is the study of the properties of triangles, including associated triangle centers, triangle lines, central circles, triangle cubics, and many others. These ...

The study of random geometric structures. Stochastic geometry leads to modelling and analysis tools such as Monte carlo methods.

Schubert's application of the conservation of number principle.

The geometry of Finsler space.

A vaguely defined branch of mathematics dealing with varieties, the Mordell conjecture, Arakelov theory, and elliptic curves.

A finite geometry is a geometry with a finite number of points. When confined to a plane, all finite geometries are either projective plane geometries (with no parallel ...