A Rubik’s Snake with General Rotation Angles

Volume 5, Issue 6, December 2021     |     PP. 123-135      |     PDF (899 K)    |     Pub. Date: November 23, 2021
DOI: 10.54647/isss12179    92 Downloads     6558 Views  

Author(s)

Songming Hou, Program of Math&Stats and Center of Applied Physics, Louisiana Tech University, Ruston, LA 71272
Scott Atkins, Louisiana School for Math, Science, and the Arts, Natchitoches, LA 71457
Yu Chen, Program of Math&Stats, Louisiana Tech University, Ruston, LA 71272

Abstract
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.

Keywords
Rubik’s Snake, robot design

Cite this paper
Songming Hou, Scott Atkins, Yu Chen, A Rubik’s Snake with General Rotation Angles , SCIREA Journal of Information Science and Systems Science. Volume 5, Issue 6, December 2021 | PP. 123-135. 10.54647/isss12179

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