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Let a cone of opening parameter c and vertex at (0,0,0) intersect a sphere of radius r centered at (x_0,y_0,z_0), with the cone oriented such that its axis does not pass ...

Given two crossed ladders resting against two buildings, what is the distance between the buildings? Let the height at which they cross be h and the lengths of the ladders ...

Let ad=bc, then Hirschhorn's 3-7-5 identity, inspired by the Ramanujan 6-10-8 identity, is given by (1) Another version of this identity can be given using linear forms. Let ...

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 Latin prefix quadri- is used to indicate the number 4, for example, quadrilateral, quadrant, etc. However, it also very commonly used to denote objects involving the ...

A quintic surface is an algebraic surface of degree 5. Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not ...

Let ad=bc, then (1) This can also be expressed by defining (2) (3) Then F_(2m)(a,b,c,d)=a^(2m)f_(2m)(x,y), (4) and identity (1) can then be written ...

The general sextic equation x^6+a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 can be solved in terms of Kampé de Fériet functions, and a restricted class of sextics can be solved in ...

The pentatope is the simplest regular figure in four dimensions, representing the four-dimensional analog of the solid tetrahedron. It is also called the 5-cell, since it ...

Araya and Wiener (2011) found the two cubic planar hypohamiltonian graphs on 70 and 88 vertices, respectively, illustrated above.