A Rubik’s Snake with General Rotation Angles

A Rubik's Snake is a toy that has been around for 40 years.It is a system of serial chain.It traditionally only allows rotations of its pieces in 90 degree increments.In this paper we are not going to restrict ourselves to these limited number of incremental rotations.We prove a theorem about the sum of rotations of a Rubik's Snake that closes on itself.We present an alternative representation for the Rubik's Snake, different from the standard representation that the toy has.We will use matrices to study the rotations of the pieces of the Rubik's Snake.In particular we will study two cases where all of the pieces of a Rubik's Snake have the same rotation angle, proving a theorem comparing the first and last pieces of a Rubik's Snake.