From the Golden Rectangle to the Fibonacci Sequences by Opher Liba & Bat-Sheva Ilany

Author:Opher Liba & Bat-Sheva Ilany
Language: eng
Format: epub
ISBN: 9783030976002
Publisher: Springer International Publishing

(3.2)

Proof

It is obvious that the following holds: .

We assume: and shall prove: :

Now, we notice that in the equations above, we only make use of the fact that satisfies the golden equation. The expression also satisfies the golden equation. Hence, we can conclude:

(3.2b)

It is worth observing the following:A.

and are normalized -numbers since they are products of normalized ϕ-numbers, c.f (1.​23) or (1.​25).

B.

is the companion of , denoted by: . As defined in Chapter 1 (1.​12a)

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