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Abel's integral is the definite integral I = int_0^infty(tdt)/((e^(pit)-e^(-pit))(t^2+1)) (1) = 1/2int_(-infty)^infty(tdt)/((e^(pit)-e^(-pit))(t^2+1)) (2) = ...

Let A_1, A_2, A_3, and A_4 be four points on a circle, and H_1, H_2, H_3, H_4 the orthocenters of triangles DeltaA_2A_3A_4, etc. If, from the eight points, four with ...

The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

The reflection circle, a term coined here for the first time, is the circumcircle of the reflection triangle. It has center at Kimberling center X_(195), which is the ...

A subset of a topological group which is closed as a subset and also a subgroup.

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

A group action phi:G×X->X is called faithful if there are no group elements g (except the identity element) such that gx=x for all x in X. Equivalently, the map phi induces ...

A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

Let T be a maximal torus of a group G, then T intersects every conjugacy class of G, i.e., every element g in G is conjugate to a suitable element in T. The theorem is due to ...

A group G is nilpotent if the upper central sequence 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... of the group terminates with Z_n=G for some n. Nilpotent groups have the property that ...