Topic: Circles in three-dimensional space
In three-dimensional space two circles are given. For each of circles are given: triple of coordinates of center; unit vector of a normal to a plane in which the circle lies; and radius. If it is pleasant to someone, it can increase at once a normal vector by radius and that the circle is set by two vectors. It is required, for the general case, to find coordinates of pair the nearest points lying on different circles. If it simplifies the decision, the cases possessing any kind of symmetry when such pairs of points more than one, it is possible to throw out from reviewing. For the cases having more of one local minimum, to find only one, giving the least distance. The task has applied relevance (in area collision detection), therefore is quite comprehensible, if the decision is received in the form of one or several transcendental equations of one variable. (Which then can be solved numerical methods and to hammer into the table). It is possible to pass from Cartesian coordinate system to any convenient (spherical, cylindrical and even actually invented specially for this task). Over this task I fought already almost about twenty years ago but so it and was not gave to me. It was possible to solve the similar task for a circle and a straight line. Here I also thought: and you never can tell, and suddenly, somebody solves.