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Although the multiplication of one vector by another is not uniquely defined (cf. scalar multiplication, which is multiplication of a vector by a scalar), several types of ...

Half of a sphere cut by a plane passing through its center. A hemisphere of radius r can be given by the usual spherical coordinates x = rcosthetasinphi (1) y = ...

The scalar triple product of three vectors A, B, and C is denoted [A,B,C] and defined by [A,B,C] = A·(BxC) (1) = B·(CxA) (2) = C·(AxB) (3) = det(ABC) (4) = |A_1 A_2 A_3; B_1 ...

While the Catalan numbers are the number of p-good paths from (n,n) to (0,0) which do not cross the diagonal line, the super Catalan numbers count the number of lattice paths ...

The word canonical is used to indicate a particular choice from of a number of possible conventions. This convention allows a mathematical object or class of objects to be ...

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 ...

In continuum theory, a dendrite is a locally connected continuum that contains no simple closed curve. A semicircle is therefore a dendrite, while a triangle is not. The term ...

A cone with elliptical cross section. The parametric equations for an elliptic cone of height h, semimajor axis a, and semiminor axis b are x = a(h-u)/hcosv (1) y = ...

An elliptic cylinder is a cylinder with an elliptical cross section. The elliptic cylinder is a quadratic ruled surface. The parametric equations for the laterals sides of an ...

A quadratic surface which has elliptical cross section. The elliptic paraboloid of height h, semimajor axis a, and semiminor axis b can be specified parametrically by x = ...