Apple

A surface of revolution defined by Kepler. It consists of more than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of the upper and lower boundaries in the - plane are

(1)

for  and . It is the outside surface of a spindle torus.

It is also a quartic surface given by Cartesian equation

(2)

or

(3) Ref: mathworld.wolfram.com

Periodogram

A graphical plot with abscissa given by the number  of consecutive numbers constituting a single period and ordinate given by the correlation ratio . The equation of the periodogram is

where each of the terms of the sequence  consists of a simple periodic part of period , together with a part which does not involve this periodicity , so

 is the standard deviation of the s,  is the standard deviation of the s, and  is the number of periods covered by the observations.

Ref: mathworld.wolfram.com