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File:Non-commutative rotation of dice.png

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Summary

Description
English: Configure two dice as shown in the upper left corner, with the 1 on top, 2 on the left, and 3 to the right. On die takes path A, beginning with a 90 degree rotation about the negative y direction (using the right hand rule), followed by a 90 degree rotation about the z direction. This leaves the die with the 5 on top, 4 on the left, and 1 to the right. But reversing the order of two paths results in 3 being on the top, 1 on the left, and 2 on the right, as shown in the lower right corner.
Date
Source Own work
Author Guy vandegrift

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Captions

A die has different orientation after two rotations, depending on which path is taken. Both path A and path B use the same rotations, but in reverse order.

Items portrayed in this file

depicts

mathematics

inception

27 December 2023

media type

image/png

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Date/TimeThumbnailDimensionsUserComment
current03:40, 28 December 2023Thumbnail for version as of 03:40, 28 December 2023884 × 1,247 (148 KB)Guy vandegriftlarger arrows
02:39, 28 December 2023Thumbnail for version as of 02:39, 28 December 2023884 × 1,247 (138 KB)Guy vandegriftUploaded own work with UploadWizard

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