Abstract.
We give an elementary proof of what is perhaps the earliest fixed point theorem; namely Leonhard Euler’s theorem of 1775 on the existence of an axis v for any three-dimensional rotation R. The proof is constructive and shows that no multiplications are required to compute v.
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Dedicated to the memory of Leonhard Euler, “The Master of us all”, on the occasion of the 300th anniversary of his birth
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Palais, B., Palais, R. Euler’s fixed point theorem: The axis of a rotation. J. fixed point theory appl. 2, 215–220 (2007). https://doi.org/10.1007/s11784-007-0042-5
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DOI: https://doi.org/10.1007/s11784-007-0042-5