Bijective sum!

This is a short, we explore the famous formula for the sum of the first n positive integers via a bijective technique.

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#sumformula #sumintegers #integers​ #mathvideo​ #math​ #mtbos​ #animation​ #theorem​ #pww​ #proofwithoutwords​​ #proof​ #iteachmath #mathematics #combinatorialproof #combinatorics #bijection

[kingklaus]

This is my favorite math channel. I love the visual proofs

[ruilopes]

I didn't realise it at first and was going to scroll down but gave it another chance... so glad that I did.

[Ninja]

It’s amazing how theres so many ways to prove this result, apart from the traditional reverse addision way.

Another way to show this combinatorially is considering n+1 dots, there n possible pairings with dot 1, n-1 new pairings with dot 2, and so on. So the total number if distinct pairings is (n+1)C2, which is actually 1+2+…+n.

[johnbutler]

Wow. I had to rewatch that to understand what was going on. That's awesome.

[Giri_Komal]

We can find it by using area formula of triangle as well . Where height is n unit and base is (n+1) unit

[vkig]

This is what I term as one of the more "painful" proofs.

I remember our university professor when telling us he was going to teach us telecommunications theory using probability, and everyone groaned. He said, "Relax, this isn't the painful probability you had dumped on you in highschool where you had to calculate inane answers like the probability of choosing a red ball out of your left pocket containing 3 blue balls and 5 red balls, while at the same time choosing a blue ball out of your other pocket containing 2 blue balls and 7 green balls, while at the same time on the other side of the street there must be three red-headed girls walking together out of a group of girls where 5 are blondes, 4 are redheads and 10 are brunettes. No, this is continuous probability, and I think you'll find it much more enjoyable!"

He was right.

[morgangraley]

I happen to understand this, but I feel like it is not accessible to the layman. Don’t get me wrong; this is an amazing video, but only seems helpful for peeps who are already math-literate.

[thejtrax]

I need information. I know that 9 to the exponent of 3 means 9 × 9 × 9. is written as 9^3 which equals 729 but what is the mathematical name or function for 9 ÷ 9 ÷ 9. which In this case equals What's it called when it's division and not multiplication

[ChrisLee-yrtz]

I don't see how that's particularly helpful.
It's much more intuitive to make an upside down copy of the triangle, align them side by side to form a slanting rectangle of dimensions n x (n+1)...

[afif]

Do you know the history of this method?