In this study I take a tour1 of rotational transformations in three-dimensions, beginning with the well-known formulae for a rotation in two dimensions. I then generalise to three dimensions, deriving a useful coordinate-free formula.

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1. 1 I declare this to be my own work, entirely. In particular, no AI was used in any research, analysis, synthesis, writing, nor typesetting of this work. In short, AI was not recruited at any time in this work. Errors and inaccuracies are therefore proudly my own.

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