• Corpus ID: 204746220

The Golden Section , Fibonacci series , and new hyperbolic models of Nature А

  title={The Golden Section , Fibonacci series , and new hyperbolic models of Nature А},
  author={L. F. Stakhov and Boris Rozin},
Приведен обзор новых математических моделей Природы, основанных на золотом сечении и использовании гиперболических функций Фибоначчи и Люка и функции «Золотой Шофар». Также рассматриваются обобщенные числа Фибоначчи, обобщенные золотые пропорции, обобщенный принцип золотого сечения, «золотые» алгебраические уравнения, обобщенные формулы Бине, непрерывные функции для обобщенных чисел Фибоначчи и Люка, матрицы Фибоначчи и «золотые» матрицы. Статья опубликована в международном электронном журнале “Visual Mathematics”, 2006, Vol. 3, No. 3 http://www.mi.sanu.ac.yu/vismath/stakhov/index.html A survey of new mathematical models of Nature is presented based on the golden section and using a class of hyperbolic Fibonacci and Lucas functions, and a surface referred to as the Golden Shofar. Also considered are generalized Fibonacci numbers, generalized golden proportions, a Generalized Principle of the Golden Section, golden algebraic equations, generalized Binet formulas, generalized Lucas numbers, continuous functions for the generalized Fibonacci and Lucas numbers, Fibonacci matrices, and golden matrices. 

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