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Let A be a set. An operation on A is a function from a power of A into A. More precisely, given an ordinal number alpha, a function from A^alpha into A is an alpha-ary ...

Let A:D(A)->H and B:D(B)->H be linear operators from domains D(A) and D(B), respectively, into a Hilbert space H. It is said that B extends A if D(A) subset D(B) and if Bv=Av ...

Given an acute angle in a right triangle, the opposite side is the leg of the triangle which is not incident on the angle. Lengths of opposite and adjacent sides appear ...

A tree is planted at each lattice point in a circular orchard which has center at the origin and radius r. If the radius of trees exceeds 1/r units, one is unable to see out ...

The four of Hilbert's axioms which concern the arrangement of points.

The central point (r=0) in polar coordinates, or the point with all zero coordinates (0, ..., 0) in Cartesian coordinates. In three dimensions, the x-axis, y-axis, and z-axis ...

An orthogonal array OA(k,s) is a k×s^2 array with entries taken from an s-set S having the property that in any two rows, each ordered pair of symbols from S occurs exactly ...

In a space E equipped with a symmetric, differential k-form, or Hermitian form, the orthogonal sum is the direct sum of two subspaces V and W, which are mutually orthogonal. ...

An "overdot" is a raised dot appearing above a symbol most commonly used in mathematics to indicate a derivative taken with respect to time (e.g., x^.=dx/dt). The expression ...

An egg-shaped curve. Lockwood (1967) calls the negative pedal curve of an ellipse with eccentricity e<=1/2 an ovoid.