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. 2017 Nov 24;29(11):2044–2050. doi: 10.1589/jpts.29.2044

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2017©by the Society of Physical Therapy Science. Published by IPEC Inc.

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives (by-nc-nd) License. (CC-BY-NC-ND 4.0: https://creativecommons.org/licenses/by-nc-nd/4.0/)

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Fig. 1. — Non-commutative property of finite rotation angles under addition. On the left, a book is placed in the Y-Z plane with the spine of the book facing to the left as its starting position. On the top middle column, the book is then rotated +90° around the x-axis (Rx), followed by a +90° rotation around the vertical y-axis (Ry). Top right: 90° + Rx + 90° + Ry=Book perpendicular to original start position with its spine facing up. Alternatively, upon reversing the order (bottom middle and right): 90° +Ry + 90°+ Rx=Book perpendicular to original start position with its spine horizontal.