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A likelihood function L(a) is the probability or probability density for the occurrence of a sample configuration x_1, ..., x_n given that the probability density f(x;a) with ...

Limacon Evolute The catacaustic of a circle for a radiant point is the limaçon evolute. It has parametric equations x = (a[4a^2+4b^2+9abcost-abcos(3t)])/(4(2a^2+b^2+3abcost)) ...

A limb of a tree at a vertex v is the union of one or more branches at v in the tree. v is then called the base of the limb.

The partial differential equation 2u_(tx)+u_xu_(xx)-u_(yy)=0.

The surface of revolution generated by the external catenary between a fixed point a and its conjugate on the envelope of the catenary through the fixed point is equal in ...

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 ...

The plane determined by the points x_1, x_2, and x_3 and the line passing through the points x_4 and x_5 intersect in a point which can be determined by solving the four ...

The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.

Also known as the first fundamental form, ds^2=g_(ab)dx^adx^b. In the principal axis frame for three dimensions, ds^2=g_(11)(dx^1)^2+g_(22)(dx^2)^2+g_(33)(dx^3)^2. At ...

The negative pedal curve of a line specified parametrically by x = at (1) y = 0 (2) is given by x_n = 2at-x (3) y_n = ((x-at)^2)/y, (4) which is a parabola.