Closed spherical curves and projection areas

Abstract

In this paper, the projection areas and the area vectors of closed spherical curves formed under a one-parameter closed spherical motion are discussed. The relation between the Steiner vector of the one-parameter closed spherical motion and the area vector of the closed spherical curve formed under the motion are given. The parallel projection area and the area vector of the closed curve formed on the fixed sphere K' by a point X on the moving sphere K are calculated. The parallel projection areas of the closed curves formed under the motion of the fixed points on an arc of a great circle on the moving sphere K are discussed and some corollaries are given.