Two properties of envelope number

Gen-Fang Chen

doi:10.1117/12.2686041

28 July 2023 Two properties of envelope number

Gen-Fang Chen

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 127560T (2023) https://doi.org/10.1117/12.2686041
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

Envelope numbers are a class of integers associated to irrational numbers, and envelope numbers have some specific properties. There is no envelope number between the two adjacent envelopes and their sum, the sum of the adjacent upper and lower envelope numbers is still the envelope numbers, and the sum of the functional values of the adjacent upper and lower envelope numbers is the functional value of their sum. The difference between the number of two adjacent envelopes is the lower envelope number, and the difference between two adjacent envelopes is the upper envelope number.

Citation Download Citation

Gen-Fang Chen "Two properties of envelope number", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 127560T (28 July 2023); https://doi.org/10.1117/12.2686041

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