The Pythonacci Matrix

by Roger Melon

I noted with interest the “The sequence, starting with 5, of every second Fibonacci number defines the lengths of the hypotenuses (c) of right triangles with integer sides (Pythagorean Triangles),” … 5 … 13 … 34 … 89 … 233 … and considered, “What, then, of the alternate Fibonacci numbers … 8 … 21 … 55 … 144 … 377 … not included in this sequence? By what subtle geometric algorithm (if, indeed, any) are they related?” In the course of this inquiry I discovered an intrinsic interrelationship, the arrangement of which I have since named The Pythonacci Matrix , for it reveals the ‘other half’ of the inherent relationship between Pyth agorean Triangles and the Fib onacci Sequence. The formulae evolved in conjunction with the development of the matrix. It is my desire that this array be disclosed, that those versed in disciplines other than my own may expound upon the fascinating correlations implicit in this seminal work. The Pythonacci Matrix assumes the reader’s basic familiarity with number theory, trigonometry, Pythagorean Triangles, and the Fibonacci Sequence.

45 pages, Paperback

Published November 4, 2020