ABSTRACT

First, let us write the equation of a torus. This surface is formed by points of a circle (1, which is moving in such a way that the center of a is moving along a circle P and the planes containing a and are mutually orthogonal. We will write the position vector r of the points of the torus in the form of a vector-function of two variables 4 and H. Let us place the circle P into the (X, y)-plane with the center of P at the origin 0 of Cartesian coordinates. Denote the radius of B by R and the radius of a by p. Let e, be unit coordinate vectors, P an arbitrary point of P and 4 an angle between el and OP. Then

O P = R(cos 4 e l + sin 4ez) .