Finding the general formula for nth octagonal number | Visual proof |

[@ThinkTwiceLtu]

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: kzbin.info/www/bejne/qWe2gaqbqsSMY7c Thank you~

[@MagicGonads]

I don't see anything wrong with it

[@denismazurak2925]

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)

[@TheJaseku]

It's great, show it to the world :)

[@TVMpedror]

The video is great! All your animations are amazing! You should make it public!

[@abaybektursun]

Dude, there should an entire playlist of math animations with lofi playing in the background

[@Mathologer]

Another nice one :)

[@ThinkTwiceLtu]

thank you:)

[@Fine_Mouche]

i will remember more easily the (2n-1)² - (n-1)² than 3n²-2n

[@ZeroKelvin]

Your videos so often make my jaw drop - thank you for making these! Wonderful!

[@ebrahimt7618]

i couldn't have imagined my mind being blown in this short amount of time great job

[@NarutoShippudenIntro]

Visual meth

[@ThinkTwiceLtu]

not even once

[@franzschubert4480]

Visual maffs

[@ThinkTwiceLtu]

maybe

[@funkysagancat3295]

I'm almost crying right now, that's so fucking beautiful

[@briann363]

Always a delight to see your vids man

[@Invalid571]

Your videos are audio visual treats. Top quality stuff! 👏 👏 ☺

[@riccardofiori828]

Totally in love with this channel ♥️

[@ThinkTwiceLtu]

[@kcfish4862]

You can also simplify it to n(3n-2) correct?

[@KingSchnarf]

Yeah that's the factored form

[@AZMaths]

good job and interesting ideas.

[@ffggddss]

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

[@NoNTr1v1aL]

Awesome video!

[@shaileshcodes]

keep up the awesome videos bro

[@ThinkTwiceLtu]

Shailesh Vasandani thanks. I'll try my best~

[@steffen5121]

Why are these numbers counted differently than hexagonal numbers?

[@wolvesgabemaster5385]

I love geometry!

[@timh.6872]

So, why do octagonal numbers share multiple verticies while other n-gonal numbers share a center? The inconsistency is a little strange.

[@Ensivion]

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.

[@chachaojrl1944]

So, try to demostrate the ecuation by induction

[@ThoughtinFlight]

DUDE!!!!! You make MART

[@NotMeInc]

What's the music?

[@danielprovder]

kinda sounds like a cover of Drake's Controlla

[@taiyoinoue]

kzbin.info/www/bejne/gIncp2R6bKt4qMU (used the shazam app)

[@Joel-id5jq]

Inmyfreetime

[@cubicardi8011]

This is too good

[@محمدحارثبھائی]

what if the shape is N-gon?

[@atomiccompiler9495]

Delightful ..

[@issamba8921]

excuse me, by which software wa can make this animation?

[@ThinkTwiceLtu]

Cinema 4d

[@rolandvankemenade5051]

Controlla

[@robertass5040]

5 math tricks that blow your mind every day

[@kristijonassakalis7771]

*6

[@ThinkTwiceLtu]

* -1

[@ameremortal5715]

Nice :)

[@tomburns5231]

Looks nice, but I have no idea what it means.

[@ducolindhout2403]

Tom Burns Haha same here, but I'm willing to learn what all if this means. Looks interesting.

[@offlinegaegt4429]

Einstein³

[@clem494949]

Watching this video without any background knowledge about octagonal numbers, I didn't understand anything.

[@whirlingbruh1489]

Why am i here?