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A polybe is a polyform formed from a polycubes by removing of half of each cube such that at least half of the original join between cubes is retained. The numbers of polybes ...

Polycairos are polyforms obtained from the Cairo tessellation, illustrated above. The numbers of polycairos with n=1, 2, ... components are 1, 2, 5, 17, 55, 206, 781, 3099, ...

For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...

The constant e^pi that Gelfond's theorem established to be transcendental seems to lack a generally accepted name. As a result, in this work, it will be dubbed Gelfond's ...

A beautiful approximation to the Euler-Mascheroni constant gamma is given by pi/(2e)=0.57786367... (1) (OEIS A086056; E. W. Weisstein, Apr. 18, 2006), which is good to three ...

A sparse polynomial square is a square of a polynomial [P(x)]^2 that has fewer terms than the original polynomial P(x). Examples include Rényi's polynomial (1) (Rényi 1947, ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

The Gregory series is a pi formula found by Gregory and Leibniz and obtained by plugging x=1 into the Leibniz series, pi/4=sum_(k=1)^infty((-1)^(k+1))/(2k-1)=1-1/3+1/5-... ...

A portion of a disk whose upper boundary is a (circular) arc and whose lower boundary is a chord making a central angle theta<pi radians (180 degrees), illustrated above as ...

The point about which an angle is measured is called the angle's vertex, and the angle theta associated with a given vertex is called the vertex angle. In a polygon, the ...