Visual Arithmetic Sums

This is a short, animated visual proof demonstrating how to visualize the sum of an arithmetic sequence, producing a closed formula for such a sum.

This animation is based on a well known visual proof technique (and it can be found in Roger Nelsen’s book Icons of Mathematics). Specializing to a = 0 and d = 1 gives the sum of the first n integers (triangular numbers) formula. Specializing to a = 1 and d = 2 gives the sum of the odd integers (which yields the squares). In general, we can get any polygonal number formula from this fact (in addition to many others).

To learn more about animating with manim, check out:

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[hemarao]

Oh the explanation with the minecraft music!
*chef's kiss

[Ninja]

The easy way to remember this formula is just the number of terms multiplied by the average of the first and last term

[marko]

Thank you for showing me that math can be interesting. I feel amazing because I understood everything you explained! Keep up this amazing work ❤

[bestsolutionlaid]

Visual math is the best way to understand evrything...

[محمدصالحعلیاکبری]

Can I have access to your animations code.
I have a question when you put many rectangles or dots together according to a pattern. Do you do this part by hard code or is there a special trick?

[kebabbert]

Gauss discovered this when he was 11 years old, in class

[Naej]

What is the purpose of a ? Or even d ? The sum could be split to end up with only the famous sum of n integers

[garimathapa]

Sum of arithmetic is n/2(2a+(n-1)d so how come the formula is different? I didn't understand.

Please reply i am trying to explain about this is my school ani i dont understand myself.

[maxime_weill]

That's crazy. p is d rotated 180°.

[Azaya]

That unexpected at the end Once the half of the rectangle rotates just beautiful Pin me please

[hr]

Found this interesting but I could not understand a single thing

[ImpossibleEvan]

Hearing "non-negitive integer" hurts

[meenasharmaJI]

Tell me which application your are using please 😢😢

[oumardiop]

prove that the sum from 0 to n of (a+id) = ((n+1)(2a+nd))/2

[baoskl]

the Minecraft music really distracted me

[Anonymous]

Banda concepts deta hai pehle aur alternate method pe bhi baat karta hai?!?

[gerardsagliocca]

You are talking too damn FAST ! I am sure you don't speak this fast when talking to friends and bosses in business environment.

I think you have somebody telling you that you must complete this teaching lecture in so many minutes, so you then decided to agree to this ridiculous stipulation, and the results are awful !


Try changing your game plan .