VM Weber | ವಿ ಎಂ ವೆಬರ್Jan 2, 2025
Philippe Smet
Don't forget to write 2025 as
1³+2³+3³+4³+5³+6³+7³+8³+9³
(next opportunity is only in 3025)!
(Or, for the #math and #LaTeX lovers:
\begin{equation}
\sum_{n=1}^9 n^3
\end{equation})
Dec 31, 2024 at 11:04amWeb
Show threadearthlingDec 31, 2024

@pfsmet

Interesting 2025

1) 2025, itself is a square (45 x 45)

2) It's a product of two squares: 9² x 5² = 2025

3) It is the sum of 3-squares: 40² + 20² + 5² = 2025

4) It's the first square after 1936 (44 x 44)

5) It's the sum of cubes of all the single digits: from 1 to 9 it would be 1³+2³+3³+4³+5³+6³+7³+8³+9³= 2025.

This is going to be our UNIQUE YEAR.

https://albertocalva.substack.com/p/next-year-2025-is-a-mathematical

#2025
#maths

Next year 2025 is a mathematical wonder

Our next calendar year is a mathematical wonder.

Alberto Calva’s Newsletter
Show threadKevin RussellDec 31, 2024

@appassionato

And (1+2+3+4+5+6+7+8+9)squared is 2025

Show threadJson DohDec 31, 2024
@kevinrns @appassionato You may include 0(zero) to the set of all single digit decimals. It will still work.
Show threadjoostetoDec 31, 2024
@pfsmet
Or for those of us who like to start counting at 0:
0³+1³+2³+3³+4³+5³+6³+7³+8³+9³=2025
Show threadRevK Dec 31, 2024
@joosteto @pfsmet well last(this) year started with (-1)³ I guess.
Show threadjoostetoDec 31, 2024
@revk @pfsmet
Indeed. But including the brackets doesn't look nice. And the brackets could be removed, but then it's like you're subtracting 1³ rather than adding (-1)³.
Show threadMans RDec 31, 2024
@joosteto @revk @pfsmet Same difference.
Show threadBytebro 🇬🇧 🇺🇦 🇬🇱Dec 31, 2024
@pfsmet
...and as I and others found when that popped up, the sum of cubes of any sequence of consecutive integers starting from 1 is always a square. Which was new to me and a joy.
Show threadTrassliga havsnöret Tomas ✅Dec 31, 2024
@pfsmet also: 45² = 2025.
Show threadVicomte Folmer af HelvedeDec 31, 2024

@pfsmet

45² also works.

But it's a bit boring 😅

Show threadKevin RussellDec 31, 2024

@folfdk

Its the sum of 123456789

Show threadJson DohDec 31, 2024
@kevinrns @folfdk boring?
45 = 20 + 25
Show threadKevin RussellDec 31, 2024

@jdoe

I don't understand. lol

Show threadlebrubruDec 31, 2024
@pfsmet Et comme par hasard (non) c'est le carré de 45 😀
Show threadClotDec 31, 2024
@pfsmet
Show threadErikPDec 31, 2024

@pfsmet and:

(1+2+3+4+5+6+7+8+9)^2 = 2025

Show threadBernd F. DollingerDec 31, 2024

@pfsmet

1) 45 x 45 or 45²

2) 9² x 5²

3) 40² + 20² + 5²

4) (1+2+3+4+5+6+7+8+9)²

5) 1³+2³+3³+4³+5³+6³+7³+8³+9³

#2025

Show threadColin the MathmoDec 31, 2024
@pfsmet For those of us on Mathstodon.... it renders LaTeX for us.
Show threadJohn Faithfull 🌍🇪🇺🏴󠁧󠁢󠁳󠁣󠁴󠁿🧡✊🏻✊🏿Dec 31, 2024
@pfsmet sounds a bit pocalyptic... 😃
Show threadJ. PetersonDec 31, 2024

@pfsmet I had to try these to believe them.

sum([math.pow(i,3) for i in range(1,10)])

math.pow(sum(range(1,10)),2)

Magic!

Show threadBryan WrightJan 1, 2025

@pfsmet

Don't forget the first term: 0^3

Show thread™Jan 1, 2025

@pfsmet Oder länger, aber Browser-kompatibel, in #MathML:

<math>
<munderover>
<mo>∑</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mn>9</mn>
</munderover>
<msup>
<mi>n</mi>
<mn>3</mn>
</msup>
<mo>=</mo>
<mn>2025</mn>
</math>

#year2025

Show threadIan RudderbuttJan 1, 2025
@pfsmet Happy Cube Year!
Show threadJan EdenJan 8, 2025
@pfsmet If Trump was a mathematician, I would assume he had this arranged for his Fourth Reich.
Show threadPypeBrosFeb 25, 2025
@pfsmet is it common to have sum(N) { i³ } = (sum(N) { i })², by the way ?
Show threadPhilippe SmetFeb 26, 2025
@PypeBros It always holds, for any n! The sum of cubes from 1³ to n³ can be expressed as n²(n+1)²/4. This is the same as (n(n+1)/2)². The sum of the first n positive integers is expressed as n(n+1)/2 (n numbers times the average of first and last, (n+1)/2. So, if you square the last expression, you get the other expression. ☐