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Let X and Y be Banach spaces and let f:X->Y be a function between them. f is said to be Gâteaux differentiable if there exists an operator T_x:X->Y such that, for all v in X, ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

In the hyperbolic plane H^2, a pair of lines can be parallel (diverging from one another in one direction and intersecting at an ideal point at infinity in the other), can ...

The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

The isoperimetric quotient of a closed curve is defined as the ratio of the curve area to the area of a circle (A=pir_A^2) with same perimeter (p=2pir_p) as the curve, Q = ...

Line segment picking is the process of picking line segments at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a ...

An orientation on an n-dimensional manifold is given by a nowhere vanishing differential n-form. Alternatively, it is an bundle orientation for the tangent bundle. If an ...

The three circumcircles through the triangle centroid G of a given triangle DeltaA_1A_2A_3 and the pairs of the vertices of the second Brocard triangle are called the McCay ...

The point of concurrence of the six planes in Monge's tetrahedron theorem.

The term "null graph" is used both to refer to any empty graph and to the empty graph on 0 nodes. Because of the conflicting usage, it is probably best to avoid use of the ...