Abstract
This note gives a proof of the Brouwer fixed point theorem by appeal to mechanical intuition. A sequence of machines is described for each real dimension greater than unity. As a sufficiently large force is applied to this mechanism, the coordinates of certain components can be made arbitrarily close to positions which are analogs of a fixed point.
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References
Scarf, M. E.,The Approximation of Fixed Points of a Continuous Mapping, SIAM Journal on Applied Mathematics, Vol. 15, pp. 1328–1343, 1967.
Eaves, B. C.,Homotopies for Computation of Fixed Points, Mathematical Programming, Vol. 3, pp. 11–22, 1972.
Zangwill, W. I.,An Eccentric Barycentric Fixed-Point Algorithm, Mathematics of Operations Research, Vol. 2, pp. 343–359, 1977.
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Communicated by R. A. Tapia
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Troutt, M.D. Conceptual machines which demonstrate the existence of Brouwer fixed points. J Optim Theory Appl 57, 537–540 (1988). https://doi.org/10.1007/BF02346170
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DOI: https://doi.org/10.1007/BF02346170