Alternating sum of squares is triangular!

This is a short, animated visual proof demonstrating how to visualize the alternating sum of squares.

#mathshorts​ #mathvideo​ #math​ #numbertheory #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #squares #triangularnumbers

To learn more about animating with manim, check out:

[dksskjshsh-ruxt]

thank you your methods really help me with my math, its because of you i got an diiferent perpesctive of sloving questions

[oddlyspecificmath]

Nice reveal, the moment the gnomons merged. Thanks !

[affaqur-rehman]

Hi, if u could plz tell me which app you use for these visuals and keep up the good work❤❤

[ajb]

I solved it in my head and it'll always be (n²+n)/2 which is the same as sum k = 1 to n of k

[sakshamsrivastava]

Isnt that summation of 1st n natural numbers

[findairy]

So wait, if the first square is n*n, and you end up with a right triangle made from half the perimeter of the first square… then the area of the leftover blocks should be (n*n)/2 right?

[maxime_weill]

nice it's not a geometric serie :p

[kennethsq]

By extension can we say that alternating sum of cubes are pyramidal numbers 🤔

[atharvyadav-uswn]

i don't want to say it but thats very...very hard to understand well i am rewatching this video for th 4th time lets see how many tryes it takes for me to understand it.