Finding the general formula for nth octagonal number | Visual proof |
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- Опубликовано: 16 сен 2024
- Sometimes creative approach leads to simple and elegant solutions...
Enjoy~
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hi, so I made another video a month ago or smth but didn't feel like it was good enough to upload. I'd still like to know what you guys think about it.
Here is the link: ruclips.net/video/s6SPweu_Y-U/видео.html
Thank you~
I don't see anything wrong with it
Well, for me it's not so obvious why integrating that area of a segment gives pi*r^2 (though I'm a bit familiar with calculus)
It's great, show it to the world :)
The video is great! All your animations are amazing! You should make it public!
Dude, there should an entire playlist of math animations with lofi playing in the background
Another nice one :)
thank you:)
i will remember more easily the (2n-1)² - (n-1)² than 3n²-2n
Visual meth
not even once
Visual maffs
maybe
Your videos so often make my jaw drop - thank you for making these! Wonderful!
I'm almost crying right now, that's so fucking beautiful
Always a delight to see your vids man
i couldn't have imagined my mind being blown in this short amount of time
great job
Your videos are audio visual treats.
Top quality stuff! 👏 👏 ☺
If it's what I think you mean, it would just be O(n) = 4n² - 4n + 1, where n = number of 'dots' on one side of the octagon.
From what I'm assuming,
O(1) = 1, just one dot;
O(2) = 1+8 = 9, the center dot + a ring of 8;
O(3) = 1+8+16 = 25, the center dot + a ring of 8 + a ring of 16; etc.
In recursive form, O(1) = 1, O(n+1) = O(n) + 8n, which yields the formula I gave.
O(n) = 8·tri(n-1) + 1 = 8·½n(n-1) + 1 = 4n² - 4n + 1
Now I watch & see what you do...
OK, that's not at all what I thought you meant.
Nice way to get the formula for this kind of number!
Fred
You can also simplify it to n(3n-2) correct?
Yeah that's the factored form
Controlla
I love geometry!
Totally in love with this channel ♥️
Why are these numbers counted differently than hexagonal numbers?
good job and interesting ideas.
Awesome video!
DUDE!!!!! You make MART
What's the music?
kinda sounds like a cover of Drake's Controlla
ruclips.net/video/JXyv1D7FErc/видео.html (used the shazam app)
Inmyfreetime
So, why do octagonal numbers share multiple verticies while other n-gonal numbers share a center? The inconsistency is a little strange.
Delightful ..
So I was thinking about this problem, and I'm not sure if I see the relation to all of the octagonal numbers. You demonstrate this with respect to the first two numbers but to extend it to higher ones could be visual trickery. I don't mean to say that this isn't true, I'm just trying to ponder how it does. I was thinking that you could treat the next octagon (O_3) with the second octagon (O_2) but there's no telling whether the pattern would actually follow from my perspective.
So, try to demostrate the ecuation by induction
This is too good
keep up the awesome videos bro
Shailesh Vasandani thanks. I'll try my best~
what if the shape is N-gon?
excuse me, by which software wa can make this animation?
Cinema 4d
5 math tricks that blow your mind every day
*6
* -1
Nice :)
Looks nice, but I have no idea what it means.
Tom Burns Haha same here, but I'm willing to learn what all if this means. Looks interesting.
Einstein³
Watching this video without any background knowledge about octagonal numbers, I didn't understand anything.
Why am i here?