The thing is, that’s NOT a “unique name” given to them by mathematicians. That’s just an English language description of them. If mathematicians had given them a name like “square-dles” or “squarities”, THAT would be a unique name used by mathematicians.
I was born in 1979, and my age squared is 2025 as well. Oh, and 44² = 45² - 45 - 44 = 2025 - 89 = 1936 and 46² = 45² + 45 + 46 = 2025 + 91 = 2116. This works with every subsequent square numbers, following the first binomial formula: (n + 1)² = n² + 2n + 1² = n² + n + (n + 1)
@@Dharun-ge2fo That what you call the "difference of two squares formula" is the third binomial formula (a + b)(a - b) = a² - b². Yes, you can use that as well: (n + 1)² - n² = [(n + 1) + n] [(n + 1) - n] = [2n + 1] [1] = 2n + 1 And to make the set complete: you can use the second binomial formula as well: (n - 1) = n² - 2n + 1² = n² - n - (n - 1)
The fact that 2025 is 45^2 has definitely been coming up in variant-sudoku. 45 is important because it's the triangular number for 9 (the sum of 1 to 9).
Every square of numbers ending with 5 is calculated by multiplying the first digit(s) with itself plus 1 and then attaching 25: 75² = 7 · 8 and attach 25, we get 5625. This can be proven with the first binomial formula: (10n + 5)² = 100n² + 100n + 5² = 100 · n · (n + 1) + 25
My mother, born in 1931 has now seen two perfect square years. That is 1936 and 2025. Most of us will only see one given that you'd need to be a minimum of 89 to have seen 44^2 and 45^2. Indeed, the great majority of those born in 1937 or the years immediately after, will not have experienced a perfect square year at all given life expectancy at the time. I will be 161 in 2116, so it seems the likelihood of me experiencing another one is a very good approximation to zero.
fun fact: this is the only square year most of us watching this video right now will ever live to see, since the next one is in 2116 and you would have to be at least 89 right now to have seen 1936
yep! that's because it is a square number, or 45x90/2. sum of a number sequence with equal intervals = amount of numbers (first number + last number) / 2 45(1+89)/2 = 45x90/2 = 45x45 = 42² square numbers are very interesting
Also, 2025 is among the first few elements in this self-referencing iterated sequence, via Domotro from Combo Class. Where T(n) is a triangular number, and with n > 1: T(2) = 3 3^2 = 9 T(9) = 45 45^2 = 2,025 T(2,025) = 2,051,325 2,051,325^2 = 4,207,934,255,625 T(4,207,934,255,625) = 8,853,355,349,833,265,389,198,125 Tn^2 = 78,381,900,950,421,300,982,881,904,787,876,752,731,430,503,515,625 k = sum of first n cubes n = 2, k = 9 n = 9, k = 2,025 n = 2,025, k = 4,207,934,255,625 k = 78,381,900,950,421,300,982,881,904,787,876,752,731,430,503,515,625
You can prove it mathematically as; (Sn)**2 equal (n(n+1)/2)**2. Expanding and rearranging can get it equal to ((n-1)*n/2)**2 + n**3. Which is equal to (S(n-1))**2 + n**3. You can then repeat the process to show that it is equal to (S(n-2))**2 + (n-1)**3 + n**3. You can continue that process to prove the identity.
@@RK-tf8pq Calculate the sum of (k+1)^4-k^4 for k varying from 1 to n : You can do it by using telescoping You can do it by simplifying (k+1)^4-k^4 and using linearity of the sum and using the formulas for the sums of k^2 and k You get a formula for the sum of the n first cubes and you can verify it's the same as (n(n-1)/2)^2
There is a Turkish politician named devlet bahçeli, back in 2009 he celebrated his party's 40th anniversary with this calculation: "There are two zeros in 2009; get rid of them what's left, 29. Scrap the zero next to 9, what's left 9 and scrap the zero next to 2 now what's left is 2. If you add 2 and 9 you get 11 and when you add 29 to 11 you end up with 40. Happy 40th anniversary of nationalist movement party (strong applause from the audience)" This video reminded to me those days.
Fun addendum to fact #1: the next year in which someone can be born so that they turn a certain age when the year is the square of that age is 2070, which is … 45 years from now, the same length of time as it is from my birth to now (I’m a lucky 1980 kid). This pattern holds, such that I was born 44 years after the last such occurrence in 1936.
I just realized another fact about 2025. All the people who turn the sum of the digits of their year of birth this year: 1) 1998: 1+9+9+8=27=3³ 2) 2016: 2+0+1+6=9=3² Both are powers of 3.
I just noticed: if you square any number between 40 and 49, the last two digits of that number will a square number two. More specific it will be the square of 50 minus that number...
Most of the interesting facts are extended from 2025=45², but it's still very interesting. 2025, being a perfect square itself, is quite a rare year since you need to wait 91 years for the next perfect square to come.
Kind of a random fact, but 4 adjacent tiles (either vertical or horizontal, it doesn’t really matter which) in Minesweeper with the numbers 2, 0, 2 and 5 respectively in them (the 0 would just be an empty space) is the last possible valid combination of numbers that represent the current year before 2100.
The cube sum of the digits never impressed me. A prime number will always be a prime number, a square number will always be a square number, but this neat little adding of cubes only works because we use base 10.
I would like to suggest a new name for the "numbers which when chopped into two parts with equal length, added and squared result in the same number" as "quadratic selfreflecting numbers". Much better, isn't it?
So, as Wendy Koopa, the fictional character, I abide by the floating timeline. I always hatched 16 years before the present day, just as Mario, Peach... actually _most_ of the main cast were born 24 years before the present day. -Yes, Mario was currently born -_-after-_ the release of Super Mario 64... die mad, or something? Anyhow, the smelly mammal _behind_ this account, was actually born in 1980... sometimes I call them "the world's oldest millennial," because there seems to be some debate as to where millennials actually start. So once I finish making them type this out for me, I should make them watch this video because it was very interesting, and indirectly about them.
Great analysis, thank you! Could you help me with something unrelated: My OKX wallet holds some USDT, and I have the seed phrase. (alarm fetch churn bridge exercise tape speak race clerk couch crater letter). Could you explain how to move them to Binance?
I had noticed that the sum of the cubes of first n number is square of total of first n numbers. I thought that I invented a new mathematical formula and even proved the formula, only to find out that the formula already exists. My proof was: the total of first n numbers is n(n+1)/2. You square it and rearrange it to show that it is ((n-1)n/2))**2 + n**3. The first term here is the square of total of first n-1 numbers. If you keep repeating this operation, you can prove the formula.
Square dates Where day² × month² = year 15 March 2025 : 15² × 3² = 2025 09 May 2025 : 9² × 5² = 2025 05 September 2025 : 5² × 9² = 2025 Last time it happened was 4 November 1936 (three that year: other two 22 February 1936 and 4 April 1936) Next time it will happen is 23 February 2116 then 24 February 2304 (one of six that year)
1) 9 = 9² 2) 9 in base 2 is 1001. 10+01 = 11, (3 in base 2). 3² is 9 3) 9 = 1³+2³ = (1+2)² 4) 9 = 1⁵×3²×4⁰ = 1+2+3+4+5-6 = 1⁸+2+3+4+5-6×7⁰ 5) In base 3: 1 22 101010, has 9 digits. [This fact as well as fact 3, if k=1³+2³+...+n³, in base n+1 when making the list up to √k will have k digits]. 443 556 is the next year n, so that n = (1+2+...+k)² and there is m so that k = (1+2+...+m)²
Here’s a good one: remove the 0. Want it back in the right place? Just multiply by 9.
WHATTT
remove the zero multiply by 2 remove the zero you will get 45
this is your year
9 is also 2+0+2+5
I was born in 1980, so I am getting a kick out of this video
Same to me🤩
By the way, you are old, just a side note reminder in case you forgot.
@@therationalanarchist I was saying he is old, I never said or thought that I was never going to get older.
Same. We turned 20 in 2000 and now we're turning 45 in 45 squared. Wow such age! :-)
But I think both of you are very young. Do you know why?@@maxhagenauer24
2:53 truly a remarkable name
The thing is, that’s NOT a “unique name” given to them by mathematicians. That’s just an English language description of them. If mathematicians had given them a name like “square-dles” or “squarities”, THAT would be a unique name used by mathematicians.
@@verkuilb it was in fact intended as a humorous statement for this very reason
@@verkuilb I think that's what Loki was saying in a different way (:
@@verkuilb bro is not getting it
@@verkuilb r/woooosh
8:33 You can also multiply by (-1)^(-2) to extend it further
That is what i want to say
I was born in 1979, and my age squared is 2025 as well.
Oh, and 44² = 45² - 45 - 44 = 2025 - 89 = 1936
and 46² = 45² + 45 + 46 = 2025 + 91 = 2116.
This works with every subsequent square numbers, following the first binomial formula:
(n + 1)² = n² + 2n + 1² = n² + n + (n + 1)
Right, everyone born in 1979 OR 1980 will be 45 years old at some point this year.
You can also use the difference of two squares formulas like 46²-45²=(46-45)(46+45), so 46²= 2025+91 = 2116, do the same for 44².
@@Dharun-ge2fo That what you call the "difference of two squares formula" is the third binomial formula (a + b)(a - b) = a² - b².
Yes, you can use that as well:
(n + 1)² - n² = [(n + 1) + n] [(n + 1) - n] = [2n + 1] [1] = 2n + 1
And to make the set complete: you can use the second binomial formula as well:
(n - 1) = n² - 2n + 1² = n² - n - (n - 1)
The fact that 2025 is 45^2 has definitely been coming up in variant-sudoku. 45 is important because it's the triangular number for 9 (the sum of 1 to 9).
Fun fact: the last time we had a square number year was 1936, the year when Hitler started his military campaign.
Ok
…and in 2025, Trump takes office.
Another equally fun fact: in 2025, Trump takes office.
Your facts aren't so fun.
In 2025, Trump takes office. Equally relevant.
7:32 i am so happy that he put in the numberblock colors
what's numberblock colors?
@@kaushalagrawal6258 Numberblocks is series about numbers it's like really good
@@kaushalagrawal6258numberblocks is a math show and the characters 1-5 are coloured red, orange, yellow, green, light blue respectively
Every square of numbers ending with 5 is calculated by multiplying the first digit(s) with itself plus 1 and then attaching 25:
75² = 7 · 8 and attach 25, we get 5625.
This can be proven with the first binomial formula:
(10n + 5)² = 100n² + 100n + 5² = 100 · n · (n + 1) + 25
That is a very fun and awesome video! Thanks, and Happy 2025 everyone! 🎉
Time traveler whats this year? Me: (1+2+3+4+5+6+7+8+9)²
Or [(9² + 9)/2]²
The square of a triangular number.
Time traveler: "Eh! Doc, this is getting pretty heavy! "
Or the sum of all the cubed integers from 1 to 9.
45²
*AD not AA(after apocalypse)
My mother, born in 1931 has now seen two perfect square years. That is 1936 and 2025. Most of us will only see one given that you'd need to be a minimum of 89 to have seen 44^2 and 45^2. Indeed, the great majority of those born in 1937 or the years immediately after, will not have experienced a perfect square year at all given life expectancy at the time.
I will be 161 in 2116, so it seems the likelihood of me experiencing another one is a very good approximation to zero.
My grandma was born 1937 and died 2024 🙁 RIP
I discovered this a few years ago. My favorite part is the 15 perfect square days this year, where each segment of the date is a perfect square.
I just noticed another fun fact: (2² + 4² + 5²)² = 2025
Ah yes, bcs 2²+4²=20
I didn't even notice that, thx ^^
Or (7²-2²)²
Along with the square of 45, the product of the proper divisors of 45 is also 2025
That’s probably because that expression simplifies to 45x45
Fact 3 is amazing. Thank you Paresh..
fun fact: this is the only square year most of us watching this video right now will ever live to see, since the next one is in 2116 and you would have to be at least 89 right now to have seen 1936
Another one I saw in another video: 2025 is the sum of the first 45 odd numbers: 1+3+5+7+ ... +89
That comes from the fact that it’s a perfect square, it would do that for any square number.
yep! that's because it is a square number, or 45x90/2.
sum of a number sequence with equal intervals = amount of numbers (first number + last number) / 2
45(1+89)/2 = 45x90/2 = 45x45 = 42²
square numbers are very interesting
10:26 the only reason this works is because 1+2+3+4+5+6+7+8+9=45 and the formula for a triangular number is ((x^2)+x)/2
This video makes me feel that the year would be good :D
Great video Presh Talwalkar
Don't know this much Pattern existed and i think there will be more 😅
But Happy New Year 2025
Good video. nice clear explanations as always!
I remember it was a (sort of) big deal that 1961 was the same right side up or upside down.
Same with 2002 (on a standard LED numeric font).
Happy New Year Presh
That was amazing!
Very cool video! 😊
Also, 2025 is among the first few elements in this self-referencing iterated sequence, via Domotro from Combo Class.
Where T(n) is a triangular number,
and with n > 1:
T(2) = 3
3^2 = 9
T(9) = 45
45^2 = 2,025
T(2,025) = 2,051,325
2,051,325^2 = 4,207,934,255,625
T(4,207,934,255,625) = 8,853,355,349,833,265,389,198,125
Tn^2 = 78,381,900,950,421,300,982,881,904,787,876,752,731,430,503,515,625
k = sum of first n cubes
n = 2, k = 9
n = 9, k = 2,025
n = 2,025, k = 4,207,934,255,625
k = 78,381,900,950,421,300,982,881,904,787,876,752,731,430,503,515,625
Umm........
It's wonderful
Thanks for the good video
very cool. Thank you!
Something wrong with u
@MarianMurphy-rz8ejlol ok buddy. Not sure why you would watch this video unless you like numbers/math patterns.
The S(n³) = (Sn)² theorem is crying out for a proof by induction.
Nah
Use a telescoping series
You can prove it mathematically as; (Sn)**2 equal (n(n+1)/2)**2. Expanding and rearranging can get it equal to ((n-1)*n/2)**2 + n**3. Which is equal to (S(n-1))**2 + n**3. You can then repeat the process to show that it is equal to (S(n-2))**2 + (n-1)**3 + n**3. You can continue that process to prove the identity.
@@RK-tf8pq Calculate the sum of (k+1)^4-k^4 for k varying from 1 to n :
You can do it by using telescoping
You can do it by simplifying (k+1)^4-k^4 and using linearity of the sum and using the formulas for the sums of k^2 and k
You get a formula for the sum of the n first cubes and you can verify it's the same as (n(n-1)/2)^2
This year is truly fascinating
2025 is a special year with a lot of mathematical characteristics.
The fact that the next square number year is after 91 years😐 only few from now will witness it
91 is a very cool number as well. It's 7 x 13. It's also a hexagonal, tetrahedral and pyramidal number.
😅😅😊😊😊😊
Would be interesting to know which next year will have all these properties.
I note that today, in standard date notation, is 1-2-25, and 1225 is the square of 35. And I note that 4-2-25, 5-6-25, and 7-2-25 are also squares.
I swear, The Hidden Path to Manifesting Financial Power is one of the best books I’ve read. It’s life-changing.
0:50 Also people born in late 1979 from now until their birthday.
The addition of 1-9 is something I'm very familiar with adding up to 45. Good tidbit to know if you play sudoku
I am watching this at 2 AM and this is what im gonna write on my final exam tommorow
is there a pattern in fact 5 that will work for range from 1 written 1 time to any natural number n written n-times, or is it just unique for 45?
I like that cubes to squares proof!
There is a Turkish politician named devlet bahçeli, back in 2009 he celebrated his party's 40th anniversary with this calculation:
"There are two zeros in 2009; get rid of them what's left, 29. Scrap the zero next to 9, what's left 9 and scrap the zero next to 2 now what's left is 2.
If you add 2 and 9 you get 11 and when you add 29 to 11 you end up with 40. Happy 40th anniversary of nationalist movement party (strong applause from the audience)"
This video reminded to me those days.
3:27 Al Khwarizmi would be so jealous
It HAS to be a good year
perfect!
Fun addendum to fact #1: the next year in which someone can be born so that they turn a certain age when the year is the square of that age is 2070, which is … 45 years from now, the same length of time as it is from my birth to now (I’m a lucky 1980 kid). This pattern holds, such that I was born 44 years after the last such occurrence in 1936.
I just realized another fact about 2025.
All the people who turn the sum of the digits of their year of birth this year:
1) 1998: 1+9+9+8=27=3³
2) 2016: 2+0+1+6=9=3²
Both are powers of 3.
The mind behind the facts is amazing. May 2025 be an auspicious year.
cool!
I just noticed: if you square any number between 40 and 49, the last two digits of that number will a square number two. More specific it will be the square of 50 minus that number...
4:49 idk why I found that so funny😂
😂 bülücübe
😗
@@Yusso idk what's funnier! the transcription, or the fact that Google translates that word as "happy birthday"
@@jamespetercharles7532 lmao
5:44
Fact 4 its so lame.. then every number can be written in terms of all digit by having power as 0
Yeah but not with exactly one occurrence per digit. Still a bit lame though
They intentionally did that to use those digits.. it’s not lame. You couldn’t even make that fact
2025 is also the Year where (a+b)^2 = the Year where a = first half of the year b = Second half of the year so a=20 b=25
2025=1⁰+2⁰+3⁰+4⁰+...+2025⁰🤯
2025 = 1¹ + 1² + ... + 1²⁰²⁵
Excellent
1^0+2^0+3^0...+2025^0 = 2025 😶
That's enough motivation for not wasting this year
Two more fun facts. The golden ratio is also in there.
Between 2025 and 3025 exactly 1000 years.
Most of the interesting facts are extended from 2025=45², but it's still very interesting. 2025, being a perfect square itself, is quite a rare year since you need to wait 91 years for the next perfect square to come.
But there's a couple more more...2025 is the product of two squares 9^2 x 5^2=2025. It's the sum of three squares 5^2+20^2+40^2=2025.
It is also 3^2+4^2+12^2+16^2+24^2+32^2=2025.
This is a crazy number
Kind of a random fact, but 4 adjacent tiles (either vertical or horizontal, it doesn’t really matter which) in Minesweeper with the numbers 2, 0, 2 and 5 respectively in them (the 0 would just be an empty space) is the last possible valid combination of numbers that represent the current year before 2100.
The cube sum of the digits never impressed me. A prime number will always be a prime number, a square number will always be a square number, but this neat little adding of cubes only works because we use base 10.
2025- Amazing mathematical year
I would like to suggest a new name for the "numbers which when chopped into two parts with equal length, added and squared result in the same number" as "quadratic selfreflecting numbers".
Much better, isn't it?
I have noticed that 2025 has 13 divisors and 5 divisors 1, 9, 25, 81, and 225 are perfect square numbers.
3:58 i was gonna comment that
So, as Wendy Koopa, the fictional character, I abide by the floating timeline. I always hatched 16 years before the present day, just as Mario, Peach... actually _most_ of the main cast were born 24 years before the present day. -Yes, Mario was currently born -_-after-_ the release of Super Mario 64... die mad, or something? Anyhow, the smelly mammal _behind_ this account, was actually born in 1980... sometimes I call them "the world's oldest millennial," because there seems to be some debate as to where millennials actually start. So once I finish making them type this out for me, I should make them watch this video because it was very interesting, and indirectly about them.
I miss the outro music. When did it stop?
Why did it stop? ??
My suggestion: Bifursqum numbers, for Bifurcate then square the sum.
Also the year of the snake
Great analysis, thank you! Could you help me with something unrelated: My OKX wallet holds some USDT, and I have the seed phrase. (alarm fetch churn bridge exercise tape speak race clerk couch crater letter). Could you explain how to move them to Binance?
I had noticed that the sum of the cubes of first n number is square of total of first n numbers. I thought that I invented a new mathematical formula and even proved the formula, only to find out that the formula already exists. My proof was: the total of first n numbers is n(n+1)/2. You square it and rearrange it to show that it is ((n-1)n/2))**2 + n**3. The first term here is the square of total of first n-1 numbers. If you keep repeating this operation, you can prove the formula.
Anyone seen CtC's video about 45²?
I
1:52 hawk 2(ah)
9:06 Someone should turn both the second and third equations into brain teasers
The fifth one is actually the 1st one explained..😂
The previous "sum of the first n cubes" date was 1296, when Edward Longshanks invaded Scotland.
He had kippers for breakfast
TRUMP2025 😮
Square dates
Where day² × month² = year
15 March 2025 : 15² × 3² = 2025
09 May 2025 : 9² × 5² = 2025
05 September 2025 : 5² × 9² = 2025
Last time it happened was 4 November 1936 (three that year: other two 22 February 1936 and 4 April 1936)
Next time it will happen is 23 February 2116
then 24 February 2304 (one of six that year)
NGL, that last one 🤯
Mabye there are other numbers with ALL the propertys of 2025?
Any 2070 kids in the chat?
Just putting the finishing touches to my time machine 😊
Me
you must feel old.. I was born in 2125. We have flying sharks now btw.
Before you post the video,I already know fact 1 and 3
uh oh. this could be the sign of a 2025 apocolypse
My being very excited over this proves that I am a nerd. 😂
2025 = 45^2... Like the "second coming" of 45. It's a sign, I tell you.
8:15 I wonder: was it worth losing time and efforts on such a clip??
I like induction better for cube sum
Fact 6: 2025 hasn’t had the same calendar as any year since 2014
I swear everyone is making these videos now lol
Fun fact: next square (46) year everyone watching this is 6 feet under.
1) 9 = 9²
2) 9 in base 2 is 1001. 10+01 = 11, (3 in base 2). 3² is 9
3) 9 = 1³+2³ = (1+2)²
4) 9 = 1⁵×3²×4⁰ = 1+2+3+4+5-6 = 1⁸+2+3+4+5-6×7⁰
5) In base 3: 1 22 101010, has 9 digits. [This fact as well as fact 3, if k=1³+2³+...+n³, in base n+1 when making the list up to √k will have k digits].
443 556 is the next year n, so that n = (1+2+...+k)² and there is m so that k = (1+2+...+m)²
If only I was born in 1980
* If only I *were* born ...
They are called tech numbers in programming stuff
I knew the first three, but not the fourth one
Save this for amc10
Surely Fact 2 numbers are called 'Presh Numbers' 🤣
Curious earthlings about their decimals 😂
Matt parker was born in 1980
A special date in this year: 4th May, 2025