Let me show you how the Fibonacci sequence has some cool patterns hiding within its last digits, and how this relates to other patterns it would have if we counted in different bases!

Here's a previous episode explaining more about how different "mods" work:    • Modular Multiplication Magic  
Here's a previous episode showing some cool links the Fibonacci sequence has with the "golden ratio":    • The Amazing Mathematics of the Golden...  

I called this "secret" in the title because many people who know the Fibonacci sequence have never heard about this awesome hidden layer to it. However, to a number theorist, it's not a "secret", and you can look up "Pisano periods" if you want to find a lot more research that has been done about this topic.

Clarification: on the title cards at about 12 minutes, when I say 2 fibonacci numbers in a row that are the "same" last digit, I don't mean the two numbers in the pair have to be the same as each other, I mean that the pair has to be the same as a previous pair we've seen before.

I've been posting some "shorts" on this channel (6 so far) without sending them to subscriptions/notification feeds, so check those out here: https://www.youtube.com/@ComboClass/s...
Also make sure you're tuned in to my @Domotro channel where I post bonus math videos and livestreams and stuff!

This was filmed by Carlo Trappenberg.
Special thanks to Evan Clark and to all of my Patreon supporters:
Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, and Jan Bosenberg!
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To join that list of people supporting this channel, and get cool bonus content, check out the Combo Class Patreon at   / comboclass  
... Supporting me there helps make the channel improve, and also helps prevent me from needing to put any sponsored ad segments within these episodes (I have turned down sponsorships from companies who would have paid me to advertise a product during these episodes).

If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you're going to send anything, please watch this short video first:    • You Can Now Mail Me Things to Put in ...  
Domotro
1442 A Walnut Street, Box # 401
Berkeley, CA 94709

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If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com

In case people search any of these terms, some of the topics discussed in this episode are: the Fibonacci sequence / Fibonacci numbers, modular arithmetic, the "Pisano periods" of the Fibonacci sequence for various different mods and its cycles related to powers of ten, how "last digits" of a number relate to its representations in different bases and different mods, etc...

If you're reading this, you must be interested in Combo Class. Make sure to leave a comment on this video so the algorithm shows it to more people :)

DISCLAIMER: Do not copy any uses of fire, sharp items, or other dangerous tools or activities you may see in this series. These videos are for educational (and entertainment) purposes.