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The functions E_1(x) = (x^2e^x)/((e^x-1)^2) (1) E_2(x) = x/(e^x-1) (2) E_3(x) = ln(1-e^(-x)) (3) E_4(x) = x/(e^x-1)-ln(1-e^(-x)). (4) E_1(x) has an inflection point at (5) ...

The extended complex plane is the name given to the complex plane with a point at infinity attached: C union {infty^~}, where infty^~ denotes complex infinity. It is also ...

Fisheye perspective is a two-part projection. First, three-dimensional space is projected onto the surface of a hemisphere, by connecting every external point to the center ...

A point related to the construction and properties of conic sections. Hyperbolas and noncircular ellipses have two distinct foci and two associated conic section directrices, ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

The term "higher dimensional group theory" was introduced by Brown (1982), and refers to a method for obtaining new homotopical information by generalizing to higher ...

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 ...

Two groups are isomorphic if the correspondence between them is one-to-one and the "multiplication" table is preserved. For example, the point groups C_2 and D_1 are ...

A planar diagram depicting a link (or knot) as a sequence of segments with gaps representing undercrossings and solid lines overcrossings. In such a diagram, only two ...

A maltitude ("midpoint altitude") is a perpendicular drawn to a side of a quadrilateral from the midpoint M_i of the opposite side. If the quadrilateral is cyclic, then the ...