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If an analytic function has a single simple pole at the radius of convergence of its power series, then the ratio of the coefficients of its power series converges to that ...

A projective correlation of period two. In a polarity, a is called the polar of A, and A the inversion pole a.

The strophoid of a circle with pole at the center and fixed point on the circumference is a Freeth's nephroid.

Taking the pole as the inversion center, the hyperbolic spiral inverts to Archimedes' spiral r=atheta.

The roulette of the pole of a hyperbolic spiral rolling on a straight line is a tractrix.

Some elements of a group G acting on a space X may fix a point x. These group elements form a subgroup called the isotropy group, defined by G_x={g in G:gx=x}. For example, ...

The polar angle on a sphere measured from the north pole instead of the equator. The angle phi in spherical coordinates is the colatitude. It is related to the latitude delta ...

The point at which the three lines connecting the polygon vertices of perspective triangles (from a point) concur, sometimes also called the homology center, pole, or, in ...

The diagonal triangle of a complete quadrangle is the triangle formed by its three diagonal points. If the quadrangle is a cyclic quadrilateral, then the circle is the polar ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...