Frau Oooo
Dan Drake 🦆I'm absurdly excited to learn that 2024 = 2³+3³+4³+5³+6³+7³+8³+9³.
...and it's because:
2025 = 45², and
45=1+2+⋯+9, and
(1+⋯+𝑛)²=1³+⋯+𝑛³ !
Via https://www.reddit.com/r/math/comments/18tr14a/2024_2³3³4³5³6³7³8³9³/.
Sparrow 🎄🎁
skategoat 🐐 🇵🇸@ddrake the Brazilian national math Olympiad had one power problem with the year every year so this brings back memories
Locomotoro@ddrake Ya decía yo...
James J Malcolm@ddrake just wait till the year after!
PepijnVemer@ddrake Just wait until 2025. 😁
dxzdb
Tom von Alten
neville park@ddrake I don't understand this but I'm happy for you all
Just Boby
Marco van Burgsteden 🍋
ChancerubbageJust a few moments I was thinking about the whole number factorization of an acre, if you need reminding of how big an acre is, can be, it’s 55 x 88 yards. Which is the appropriate number of divisors 11, 5, 3, and 2 in feet (8 is 2x2x2x2) . You can make an acre less square than 5x8, but many of those shapes will happen to divide evenly and neatly into a square mile, based on another seemingly arbitrary distance of 5,280 feet.
kasperdIt will be even better a year from now when we can add one or two more terms in front.
Of course we could also add three more terms in front now and still get 2024.
Of course we could also add three more terms in front now and still get 2024.
Blobster@ddrake Nice, thanks!
BTW, do you know of a convenient way on Linux (maybe using LaTeX-style markup) to enter equations as in your message, with the Unicode math characters (the special 𝑛 aka U+1D45B MATHEMATICAL ITALIC SMALL N, integer powers, etc.)?
P.S.: Those who wonder why (1+⋯+𝑛)²=1³+⋯+𝑛³ can sum the relations
(𝑘(𝑘+1)/2)² − (𝑘(𝑘−1)/2)² = 𝑘³
for 𝑘 from 1 to 𝑛.
Colin the Mathmo@blobster I don't know if this is specific to my instance -- Mathstodon -- but when I use the regular web app to enter stuff, it has an option for converting LaTeX markup to Unicode -- see the screenshot.
@ddrake Thanks for your reply! Indeed, I believe this feature is specific to your instance.
@blobster it is, but we're not selfish. 🙂 You can contact @christianp for details; @mwt has it working for their amusingly-named econtwitter mastodon instance...
shower thought: with The Site That Was Twitter now being called X, I like the idea that "twitter" could be a generic term for this kind of social media site, revolving around short-ish posts/tweets that are usually visible to everyone.
(This matches interestingly with Cory Doctorow's ideas of breaking up social media companies, of interoperability, and also matches the language he uses in his recent book The Lost Cause, where he uses "the twitters" to refer to just this kind of idea.)
Hash@ddrake
Heart broken
Heart broken
@ddrake
What numbers may yield less violence?
What numbers may yield less violence?
LillyLyle/Count Melancholia@ddrake So ... is that good or bad ? 😊
Brian DearI kinda don’t like hearing that 2025 is 45 squared. 🤔
myrmepropagandist
moondog548
Zalasur 🐸🇺🇦@futurebird @ddrake Huh, did a quick check and the last time we had a perfect square year was 1936. The next one will be 2116.
@futurebird @ddrake I'd say the same is true for virtually anyone old enough to read this post
Coles Street Pothole@futurebird @zalasur @ddrake Heh, way back in the early days, folks who lived an average age saw six, while folks who lived to a ripe age saw eight or nine!
KT controls miniature worlds@ColesStreetPothole @futurebird @zalasur @ddrake
Well... I got to see two palindrome years! So there's that.
Well... I got to see two palindrome years! So there's that.
@KinkyTurtle @futurebird @zalasur @ddrake And the next one isn't for a while—let's see how many Rush fans can stay alive until it occurs.
TrickTim@zalasur @futurebird @ddrake
So correlation tells me the Nazis rise is caused by the perfect square years.
So correlation tells me the Nazis rise is caused by the perfect square years.
Chris Rauh
Bruce Elrick@chrisrauh @futurebird @ddrake
This is the money shot.
RevK 
@chrisrauh I did not know that formulae and that is such a clear graphic to explain it so simply.
John Harris
Eva Harasta@ddrake Oh to be 45 in 2025! (My best friend would have been 45. I will be 48, what can I say.)
Pepper 🐾@ddrake @scottymax check it.
@ddrake This is a great fact about 2025. You seem to be celebrating it a year too soon.
EineKleine@ddrake And a year from now, add 1^3 to complete the series!
Lorelei@otheorange_tag Apparently, there’s going to be maths in the new year … 😳
Harm Botjes@ddrake eh? (1+2)^3=1^3+3^3= 1*1*1+2*2*2=1+8=9
Why not 3^3=3*3*3=27 ?
Why not 3^3=3*3*3=27 ?
Karen Campe@ddrake love it!!
It's also a difference of 2 squares:
2024 factors into 2^3•11•23
Rearrange into (2•23)(4•11)
46•44
(45 + 1)(45 – 1)
45^2 – 1^2
2025 – 1
2024
It's also a difference of 2 squares:
2024 factors into 2^3•11•23
Rearrange into (2•23)(4•11)
46•44
(45 + 1)(45 – 1)
45^2 – 1^2
2025 – 1
2024
Alan Bellingham@ddrake You could start a few terms earlier.
2024 = (-1)³+0³+1³+2³+3³+4³+5³+6³+7³+8³+9³
Pierre Jiji
The Animal and the Machine
Andy Randall 🇺🇦
olligobber@ddrake I have a geometric proof of ∑(𝑖³)=(∑𝑖)² that I should really write up....
AkaSci 🛰️@ddrake
Check out https://numbers-magic.com/?p=11269 for the delightfully many numerical representations of 2024 (and 24) .
E.g., -
Check out https://numbers-magic.com/?p=11269 for the delightfully many numerical representations of 2024 (and 24) .
E.g., -
tommy
Robin Doody@ddrake Last year was maybe tidier at 7x17².
Duncan Murray@ddrake Very cool!
Dave Carlson@ddrake a python two-liner...
`>>> nums = list(range(2, 10, 1))`
`>>> sum([num**3 for num in nums])`
## 2024
Dima Pasechnik 🇺🇦 🇳🇱@beepcheck @ddrake
1-liner, which also takes less memory, as it never produces all of nums at once:
sum(n**3 for n in range(2,10))
it's actually about 25% faster to do
sum(map(lambda n: n**3, range(2,10)))
- but the difference will only be seen on much bigger ranges
Art Smart@ddrake I'll double check it, but before I do, let me note that at the end of your fourth equation, you should remove the exclamation point, as it implies a factorial. I realize you meant it for emphasis, but the factorial makes the equation incorrect.
@ArtSmart ack!
The use of exclamation points in mathematical prose is the bane of my existence, because (1) I'm a combinatorics person, and hence love factorials; (2) am usually pretty excited when I write about math.
So, I am *constantly* in agony about the ambiguity of ending a sentence that contains an equation with an exclamation point.
You could just do periods after factorials, and get things like:
We know that 6 = 3!.
But of course, then if you are excited, you get a similar problem:
We know that 6 = 3!!
(Is that "3 factorial, exclamation point", or 3 double factorial?)
@ddrake I hear you. And yes, 3!! = 6! = 720
Whichever mathematician thought of using the exclamation point for factorials didn't really think it through, I guess. Bummer
Don't forget you can edit your toot to remove the errant exclamation point