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An authalic latitude given by phi_g=tan^(-1)[(1-e^2)tanphi]. (1) The series expansion is phi_g=phi-e_2sin(2phi)+1/2e_2^2sin(4phi)+1/3e_2^3sin(6phi)+..., (2) where ...

The Hamming distance between two vertices of a hypercube is the number of coordinates at which the two vertices differ.

The necessary and sufficient condition that an algebraic curve has an algebraic involute is that the arc length is a two-valued algebraic function of the coordinates of the ...

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...

To predict the result of a measurement requires (1) a model of the system under investigation, and (2) a physical theory linking the parameters of the model to the parameters ...

The Kiepert hyperbola is a hyperbola and triangle conic that is related to the solution of Lemoine's problem and its generalization to isosceles triangles constructed on the ...

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

An image of an object obtained by reflecting it in a mirror so that the signs of one of its coordinates are reversed.

Multi-index notation is used to shorten expressions that contain many indices. Let x in R^n and write x=(x_1,...,x_n). A multi-index alpha is an n-tuple of integers alpha_j ...

A quadratic surface given by the equation x^2+2rz=0.