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14 June 2023 Generalization of Steinhaus conjecture
Gen-Fang Chen
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Proceedings Volume 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023); 1272512 (2023) https://doi.org/10.1117/12.2678950
Event: International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 2023, Suzhou, China
Abstract
H. Steinhaus proposed a conjecture about irrational numbers, called the Steinhaus conjecture. Sós et al. proved it, and the results of the study are referred to as the “Three Gap Theorem.” In this paper, we promote the Steinhaus conjecture and prove the generalization of the Three Gap Theorem, in which the definition domain of independent variables is extended from natural number sets to integer sets, and an application of the extended conclusion in the field of music art is illustrated.
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Gen-Fang Chen "Generalization of Steinhaus conjecture", Proc. SPIE 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 1272512 (14 June 2023); https://doi.org/10.1117/12.2678950
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