Followup article:   / findingtheindexoffibonaccinumbers  

Solving for the bounds on the height of a balanced binary tree, deriving a proof for Binet's formula, and finding room for improvement in Donald Knuth's "The Art of Computer Programming".

Corrections:
13:16 These are the first and ZEROTH Fibonacci numbers

Animated with:
The Manim Community Developers. (2021). Manim – Mathematical Animation Framework (Version v0.12.0) [Computer software]. https://www.manim.community/

Matt Parker's video on complex Fibonacci numbers:    • Complex Fibonacci Numbers?  

Music: Erik Satie's Gnossienne No. 5 Performed by Cleo's Piano

Chapters:
00:00 Introduction
00:21 Some Quick Definitions
01:50 The Question
02:19 The Lower Bound
04:24 The Upper Bound
07:49 Deriving Binet's Formula
15:47 The Solution
17:07 The Discovery