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The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

Given a circle, the apothem is the perpendicular distance r from the midpoint of a chord to the circle's center. It is also equal to the radius R minus the sagitta h, r=R-h. ...

The term "cylinder" has a number of related meanings. In its most general usage, the word "cylinder" refers to a solid bounded by a closed generalized cylinder (a.k.a. ...

A major arc (right figure) is an arc of a circle having measure greater than or equal to 180 degrees (pi radians).

A minor arc (left figure) is an arc of a circle having measure less than or equal to 180 degrees (pi radians).

The perpendicular distance h from an arc's midpoint to the chord across it, equal to the radius R minus the apothem r, h=R-r. (1) For a regular polygon of side length a, h = ...

The areas of the regions illustrated above can be found from the equations A+4B+4C=1 (1) A+3B+2C=1/4pi. (2) Since we want to solve for three variables, we need a third ...

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...

A Smith number is a composite number the sum of whose digits is the sum of the digits of its prime factors (excluding 1). (The primes are excluded since they trivially ...

A permutation matrix is a matrix obtained by permuting the rows of an n×n identity matrix according to some permutation of the numbers 1 to n. Every row and column therefore ...