6 August 2024

Transfiguration of Our Lord; Sts. Sixtus II, Felicissimus & Agapitus 258 AD

In this part, I will focus on the Fibonacci-like sequences and in the second part on their geometrical representation, i.e., spirals. Using the multiplication/division tables and summation/subtraction tables in a certain way will let us get exact values of the Fibonacci-like sequences, and, what is quite interesting fractional Fibonacci-like sequences, unknown until this day. I will present a way to get these transformations done. The examples will follow. I will choose a couple of basic sequences for everyone to see how it works.

How is it possible? Well, each entry in the multiplication/division tables and in the summation/subtraction tables is a very special number with properties of a Fibonacci sequence, which, in turn, can be represented geometrically as a Fibonacci-type spiral with a unique ‘golden ratio’. This fact goes a bit against the linearity of the whole system using the superposition principle. As you saw in three previous articles, the exponents on entries were not equal to one but slightly larger or smaller than one, i.e., non-linear.

There will be a minimum of three articles on Fibonacci-like sequences. Hopefully, the reader will find these pages entertaining and educational at the same time.

Sint-Salvators Cathedral (Bruges, Belgium) - statue of God the Eternal Father by sculptor Artus Quellinus the Younger:

The Ambrosian Hymn ‘Te Deum Laudamus’ by Tu Es Petrus

>>>   https://www.youtube.com/watch?v=2nibbu6ACU0&list=LL&index=22