Hypertriangular Numbers

How many dimensions can a number be "hypertriangular" in? Let me show you how that question leads to some incredible facts, connections, and mysteries... This episode was created entirely by me (Domotro). I designed all of the graphics and other visuals, made all of the music, filmed it all, edited it, etc. Correction: with the text that listed specific dimensions of 3003, I accidentally put 3001D when that dimension should say 76D instead. The rest of them (and overall number of them) are correct. To learn more about some subtopics from this video, also check out these videos: Fractals in Pascal's triangle: https://youtu.be/VE-lKj9tF4k Fibonacci sequence cycles: https://youtu.be/8W1eSYiVHqU Factorial facts: https://youtu.be/b2zhTrggRDE If you enjoy my videos, please consider supporting on Patreon (or on the Youtube memberships on my @Domotro channel) : https://www.patreon.com/comboclass (You will get your name in the credits of my upcoming, and also get some secret bonus content. And in general it helps me to continue making videos that don't include any sponsorships from companies.) Catch up on the earlier episodes of Grade -3 with this chronological playlist: https://www.youtube.com/playlist?list=PLsATqXCEHAboWuDWuwrPGA0ZsiGNPOOvd (the "playlists" section of this channel also has playlists for Grade -1 and Grade -2, and some other playlists related to different topics) Bonus channel: https://www.youtube.com/@Domotro Combo Class Discord: https://discord.gg/nMxjCEhhFn Subreddit: https://www.reddit.com/r/comboClass My email (for potential collaborations or stuff) is on the about page of this channel. Feel free to email me, but I may not reply right away. Disclaimer: Do not copy anything involving fire that you may see in this video. Some rough timestamps of different parts, which I'll probably update later to be more clear chapters (although I do hope you watch the whole thing in order!) 0:00 - hypertriangular shapes 2:00 - iterated triangular numbers 4:20 - counting edges and faces 5:22 - Pascal’s triangle of triangles of triangles 7:31 - binomial coefficients and powers of 11 9:05 - how many ways you can choose things 11:40 - trivial and symmetrical hypertriangularities 13:34 - small numbers with not enough room 15:00 - the interesting thing about 10 16:14 - the missing odd levels 17:30 - numbers that are 2D and 3D hypertriangular 18:30 - a strangely enormous gap 19:44 - connections to the Fibonacci sequence 23:06 - members of a large infinite family 24:35 - Singmaster’s conjecture 25:55 - mysterious results of empirical testing 27:28 - which levels are easy or rare to construct 28:40 - alternate views and metrics 29:39 - bonus cloverquest follow-up and outro