2025 will be an interesting year . . . (Nichomachus's Theorem)

[@tdiogo_gamer]

You are going to go viral one day, remember us

[@macaroni_slaparoni]

Agreed. Remember us OGs.

[@Redstoner34526]

Agreed

[@PaNdaManBS]

Agreeed.

[@triniasta]

i waanna be remembered

[@Gimmickvr]

Yeah

[@macaroni_slaparoni]

A short and simple video for a short and simple topic. 0:24 was a super cute touch.

[@michaelcai254]

At 3:05 we can also note that both terms have a factor of (k+1)^2, which makes the numerator equal to (k^2 + 4k + 4)(k+1)^2 = (k+2)^2 (k+1)^2. makes the factoring a bit easier. love your videos btw! :D

[@Zscore6174]

Oh wow, didn't even realize! I ended up factoring the hard way. And thanks for the support, it means a lot!

[@triniasta]

fun fact about 2024: 2024 is actually a tetrahedral number meaning its a sum of the first n triangle numbers, or a sum of the sums of the first n natural numbers. (so like (1)+(1+2)+(1+2+3)+(1+2+3+4)+...)

[@trwn87]

Here is a new subscriber, well-earned! ALSO, cats are nice!

[@Its_Zer0here]

Came here for nichomachus's theorem ❌ Came here for the soothing voice ✅

[@theforestita2376]

Loved this!

[@IsaacDickinson-tf8sf]

Today, every way to write the date contains only square numbers

[@derelbenkoenig]

Well... Writing the date in the Julian calendar or the Hebrew calendar or the Chinese calendar are also ways to write today's date

[@Redstoner34526]

Another great video from the goat 🗣️

[@pedropiata648]

A thing thats cool is that 2025=45²=(20+25)²=(1+2+...+9)² This will also happen in 3025 (as said in the tumbnail) 3025=55²=(30+25)²=(1+2+...+10)² 🤯🤯

[@muskyoxes]

It's not at all clear to me that a general cube would lay out in just the right L shape. I guess i can revert to algebra. The corner is n^2. Each leg is width n and height sum of numbers to n-1, so add them all up: n^2 + 2 * [ n * (n(n-1)/2) ] = n^2 + n^3 - n^2

[@basta84]

Interestingly, 2024 can also be written as the sum of cubes, namely starting from -1 up to 9. However, I am pretty sure that Nichomachus's theorem fails when starting at a negative number.

[@keikoyamamoto4313]

Yeah, I think it has to start at 1. (Or 0 technically but that’s trivial)

[@keikoyamamoto4313]

Math Olympiad competitors: write that down!

[@JoeCoup1]

Fun video !

[@michaelbennett5568]

Neat.

[@patrickstar236]

Hi😊

[@ilmuoui]

AI can proofread better than bro

[@macaroni_slaparoni]

AI can also come up with more creative and factually based insults...