The present contribution exhibits fundamental and exact structures in the distribution of Fibonacci summands as the structures themselves manifesting as strictly Fibonacci generated. Basically, the summands, both as (first) ordinal and as (second) cardinal numbers, are constituted from stepwise tandem between Fibonacci ordinal and cardinal numbers. The exhibition reveals that the distribution of summands is generated in formal congruence with Pascal’s triangle, thus indicating a reinterpretation of Pascal’s triangle as a Fibonacci-generated epistructure. This reinterpretation, as well as some other results from deeper contemplation of structures involved in Fibonacci generation of the distribution of summands, are shortly discussed in relation to some more recent advances in related mathematics and science, not excluding the previous attempt of the author to systematically reconstitute the foundations of number theory as generated from a deeper and more abstract conception of the Fibonacci algorithm.

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Fibonacci Generation of Exact Distribution of Fibonacci Summands

  • Stein E. Johansen

摘要

The present contribution exhibits fundamental and exact structures in the distribution of Fibonacci summands as the structures themselves manifesting as strictly Fibonacci generated. Basically, the summands, both as (first) ordinal and as (second) cardinal numbers, are constituted from stepwise tandem between Fibonacci ordinal and cardinal numbers. The exhibition reveals that the distribution of summands is generated in formal congruence with Pascal’s triangle, thus indicating a reinterpretation of Pascal’s triangle as a Fibonacci-generated epistructure. This reinterpretation, as well as some other results from deeper contemplation of structures involved in Fibonacci generation of the distribution of summands, are shortly discussed in relation to some more recent advances in related mathematics and science, not excluding the previous attempt of the author to systematically reconstitute the foundations of number theory as generated from a deeper and more abstract conception of the Fibonacci algorithm.