Phi and the TRIBONACCI monster @Mathologer

Uploaded December 2017 | Updated September 2026, 2 weeks ago

NEW (Christmas 2019). Two ways to support Mathologer
Mathologer Patreon: patreon.com/mathologer
Mathologer PayPal: paypal.me/mathologer
(see the Patreon page for details)

Today's video is about explaining a lot of the miracles associated with the golden ratio phi, the Fibonacci sequence and the closely related tribonacci constant and sequence.

Featuring the truely monstrous monster formula for the nth tribonacci number, the best golden ratio t-shirt in the universe, rabbits, mutant rabbits, Kepler's wonderful Fibonacci-Phi link, Binet's formula, the Lucas numbers, golden rectangles, icosahedra, snub cubes, Marty, a very happy Mathologer, etc.

Special thanks to my friend Marty Ross for some good-humoured heckling while we were recording the video and Danil Dimitriev for his ongoing Russian support of this channel.

Also check out my other videos featuring the golden ratio and the Fibonacci numbers.

The fabulous Fibonacci flower formula: youtu.be/_GkxCIW46to

Infinite fractions and the most irrational number (phi): youtu.be/CaasbfdJdJg

Enjoy!

$Phi and the TRIBONACCI monster NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Todays video is about explaining a lot of the miracles associated with the golden ratio phi, the Fibonacci sequence and the closely related tribonacci constant and sequence. Featuring the truely monstrous monster formula for the nth tribonacci number, the best golden ratio t-shirt in the universe, rabbits, mutant rabbits, Keplers wonderful Fibonacci-Phi link, Binets formula, the Lucas numbers, golden rectangles, icosahedra, snub cubes, Marty, a very happy Mathologer, etc. Special thanks to my friend Marty Ross for some good-humoured heckling while we were recording the video and Danil Dimitriev for his ongoing Russian support of this channel. Also check out my other videos featuring the golden ratio and the Fibonacci numbers. The fabulous Fibonacci flower formula: https://youtu.be/_GkxCIW46to Infinite fractions and the most irrational number (phi): https://youtu.be/CaasbfdJdJg Enjoy!$

Power sum MASTER CLASS: How to sum quadrillions of powers ... by hand! (Euler-Maclaurin formula)

Multiplying monkeys and parabolic primes

Math is Illuminati confirmed (PART 2): Morleys Miracle

The hardest What comes next? (Eulers pentagonal formula)

Pi is IRRATIONAL: simplest proof on toughest test

Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.

$Ramanujans infinite root and its crazy cousins In this video Ill talk about Ramanujans infinite roots problem, give the solution to my infinite continued fraction puzzle from a couple of weeks ago, and let you in on the tricks of the trade when it comes to making sense of all those crazy infinite expressions. Featuring guest appearances by Viharts infinite Wau fraction, the golden ratio and the Mandelbrot set. Here is a link to a screenshot of Ramanujan’s original note about his infinite nested radical puzzle: http://www.qedcat.com/misc/ram_incomplete.jpg Check out the following videos referred to in this video: https://youtu.be/jcKRGpMiVTw Mathologer video on Ramanujan and 1+2+3+... 1/12. This one also features an extended discussion of assigning values to infinite series in the standard and a couple of non-standard ways https://youtu.be/CaasbfdJdJg Mathologer video on infinite fractions and the most irrational of all irrational numbers. https://youtu.be/9gk_8mQuerg Mathologer video on the Mandelbrot set. The second part of this one is all about a supernice way of visualising the infinite expression at the heart of this superstar. https://youtu.be/GFLkou8NvJo Vi Harts video on the mysterious number Wau, a must-see :) Enjoy :)$

The 3-4-7 miracle. Why is this one not super famous?

Why do mirrors flip left and right but not up and down?