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MATHEMATICAL MODELING AND NUMERICAL SIMULATION
Ray trajectories, binomial coefficients of a new type, and the binary system
A. V. Yurkin The Institute of Mathematical Problems of Biology RAS, IMPB RAS, 4, Institutskaja str., 142290, Pushchino, Moscow Region, Russia
Abstract:
The paper describes a new algorithm of construction of the nonlinear arithmetic triangle on the basis of numerical simulation and the binary system. It demonstrates that the numbers that fill the nonlinear arithmetic triangle may be binomial coefficients of a new type. An analogy has been drawn with the binomial coefficients calculated with the use of the Pascal triangle. The paper provides a geometrical interpretation of binomials of different types in considering the branching systems of rays.
Keywords:
nonlinear arithmetic triangle, binary system, binomial coefficients, branching systems of rays, lasers.
Received: 27.06.2010
Citation:
A. V. Yurkin, “Ray trajectories, binomial coefficients of a new type, and the binary system”, Computer Research and Modeling, 2:4 (2010), 359–367
Linking options:
https://www.mathnet.ru/eng/crm609 https://www.mathnet.ru/eng/crm/v2/i4/p359
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Abstract page: | 56 | Full-text PDF : | 36 | References: | 14 |
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