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Symmetric points are preserved under a Möbius transformation. The Schwarz reflection principle is sometimes called the symmetry principle (Needham 2000, p. 252).

An ordered finite configuration with certain pairs of points, called cables, which are constrained not to get further apart and certain other pairs of points, called struts, ...

f(x)=1-2x^2 for x in [-1,1]. Fixed points occur at x=-1, 1/2, and order 2 fixed points at x=(1+/-sqrt(5))/4. The natural invariant of the map is rho(y)=1/(pisqrt(1-y^2)).

Let graph G have p points v_i and graph H have p points u_i, where p>=3. Then if for each i, the subgraphs G_i=G-v_i and H_i=H-u_i are isomorphic, then the graphs G and H are ...

A set of identities involving n-dimensional visible lattice points was discovered by Campbell (1994). Examples include product_((a,b)=1; ...

The above topological structure, composed of a countable union of compact sets, is called Alexander's horned sphere. It is homeomorphic with the ball B^3, and its boundary is ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points. The second derivative of each polynomial is commonly ...

The computation of points or values between ones that are known or tabulated using the surrounding points or values. In particular, given a univariate function f=f(x), ...

A knot diagram is a picture of a projection of a knot onto a plane. Usually, only double points are allowed (no more than two points are allowed to be superposed), and the ...