tinuous mass. For most cases, the number of degrees of freedom is six, as three coordi- nates are needed to locate the body´s center of mass and three more to describe its ori- entation [1],[2]. But if the mass is all dis- tributed along a single line, then it will be impossible for the body to rotate about that line, and therefore, such a body has only five degrees of freedom [2],[3]. A similar reasoning is used to calculate N$_{3}$ , after assuming that S$_{3}$ may be viewed as a sole body instead of a collection of particles. Hence, N$_{3}$ is five when n = 2, since the mass points lie all along the same line, and is six when n > 2 [4]. The case in which n > 2 particles lie all on the same line will not be considered in this work. This same results should be attainable through individual consideration of the par- ticle which make up S$_{3}$ . Counting the num- ber of degrees of freedom of S$_{3}$ is fairly easy when n is equal to two: six are the coordi- nates needed to locate the centers of mass of the particles, but there is one restriction (one rigid link), so the number of degrees of freedom of S$_{3}$ is five. It is not hard either to calculate the number of degrees of freedom of S$_{3}$ when n = 3. Then, nine coordinates are needed to specify the positions of the parti- cles´centers of mass, but since there are three restrictions, the number of degrees of freedom is six. That is, if the triad does not lie all along the same line; if that is so, there are But when a second particle is taken into consideration, to express that the distances between this and the other particles remain constant, only n − 2 equations are needed, because the equation that shows that the dis- tance between particles 1 and 2 is constant is already included in (1). If a third particle is considered, there would be n − 3 equations more; for a fourth particle, there would be n − 4 equations more, and so on. In total, four restricitions and the number of degrees of freedom of the system is again five. The operation of calculating N$_{3}$ by con- sideration of the individual particles would be much easier if an expression which would yield the number of degrees of freedom of S$_{3}$ for any given value of n was developed. Al- bert Einstein figures among those who tried to develop an expression such. Einstein dealt with this problem in one of his books [5], us- ing it as an example of the importance that geometrical concepts have a correspondence with real objects. He reasoned more or less along the following lines: If one particle (let this particle be called particle 1), is arbitrarily chosen from among the n that compose S$_{3}$ , n − 1 equations are needed to express the fact that this particle holds fixed distances with the rest where d is a constant and j = 1 , 2 , 3 , ..., n ( x$_{j}$ − x$_{1}$ ) 2 + ( y$_{j}$ − y$_{1}$ ) 2 + ( z$_{j}$ − z$_{1}$ ) 2 = d (1) 2