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Through any point in the plane, there is at most one straight line parallel to a given straight line. This axiom is equivalent to the parallel postulate.

The addition of two quantities, i.e., a plus b. The operation is denoted a+b, and the symbol + is called the plus sign. Floating-point addition is sometimes denoted direct ...

A real function is said to be analytic if it possesses derivatives of all orders and agrees with its Taylor series in a neighborhood of every point.

A retraction is a continuous map of a space onto a subspace leaving each point of the subspace fixed. Alternatively, retraction can refer to withdrawal of a paper containing ...

In any triangle, the locus of a point whose pedal triangle has a constant Brocard angle and is described in a given direction is a circle of the Schoute coaxal system.

If a line L is the Simson line of a point P on the circumcircle of a triangle, then P is called the pole of L (Honsberger 1995, p. 128).

A surveying problem which asks: Determine the position of an unknown accessible point P by its bearings from three inaccessible known points A, B, and C.

The placement of n points on a sphere so as to minimize the maximum distance of any point on the sphere from the closest one of the n points.

Let (x_0,y_0) be any point of a surface function z=f(x,y). Then the surface has a nonvertical tangent plane at (x_0,y_0) with equation ...

The tritangent of a cubic surface is a plane which intersects the surface in three mutually intersecting lines. Each intersection of two lines is then a tangent point of the ...