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Infinite series of various simple functions of the logarithm include sum_(k=1)^^^inftylnk = 1/2ln(2pi) (1) sum_(k=1)^^^infty(-1)^klnk = 1/2ln(1/2pi) (2) ...

A logarithmic singularity is a singularity of an analytic function whose main z-dependent term is of order O(lnz). An example is the singularity of the Bessel function of the ...

There are several types of numbers that are commonly termed "lucky numbers." The first is the lucky numbers of Euler. The second is obtained by writing out all odd numbers: ...

An elliptic curve of the form y^2=x^3+n for n an integer. This equation has a finite number of solutions in integers for all nonzero n. If (x,y) is a solution, it therefore ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

The Neuberg cubic Z(X_(30)) of a triangle DeltaABC is the locus of all points P whose reflections in the sidelines BC, CA, and ABform a triangle perspective to DeltaABC. It ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

The orthocentroidal circle of a triangle DeltaABC is a central circle having the segment joining the triangle centroid G and orthocenter H of DeltaABC as its diameter ...

Flat polygons embedded in three-space can be transformed into a congruent planar polygon as follows. First, translate the starting vertex to (0, 0, 0) by subtracting it from ...

In the case of a general surface, the distance between two points measured along the surface is known as a geodesic. For example, the shortest distance between two points on ...