If you allow negatives this can actually go much further. This is the best I've gotten so far: 3^(-4)x(-1)⁸x(-3)^(-6)x9⁷x(-5)^(-2)x5⁴x1²x6⁰ It might be possible to push this even more but I can't be bothered I've already wasted too long on this lol
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.
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).
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)
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
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
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.
@@kinkinawesome If a number has 6 factors then it's square is product of proper factors Take 28 which has factors 1,2,4,7,14,28. Take product of 2,4,7,14 which is 28^2
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
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.
fun fact I found myself, for the last one, if you go to 44 instead of 45 you have 1935 which is one digit under 1936 (remember, 44^2) and if you go to 46, you have 2117, which is one digit over 2116 (which is 46^2) !!
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.
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.
This is incredible 😢 Fun fact: 99999999999999980000000000000001 Split in half and add 9999999999999998 + 0000000000000001 =9999999999999999 9999999999999999 power 2 =99999999999999980000000000000001 (The first number) Same happens with 2025 😊
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.
I can see you are implicitly using "mathematical induction," as ancient Greek mathematicians used to. To be rigorous, you need also to state the base case.
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...
And the first two digits of the square are 25 minus the difference between the number and 50, because (50-x)^2 = 100(25-x) + x^2 so you can mentally compute those squares this way. Also, you can make a similar observation about the squares of 51 through 59.
As an average of 2 cousin primes, whose square is the year: 43*47 = 2021 is only 4 years ago The other two neighbors: 37*41 = 1517 67*71 = 4757 Twin primes dont even come close to today: 41*43 = 1763 59*61 = 3599
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.
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?
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
Instead of x9 , /1111 to get repeating decimal :)
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
8:33 You can also multiply by (-1)^(-2) to extend it further
That is what i want to say
If you allow negatives this can actually go much further. This is the best I've gotten so far:
3^(-4)x(-1)⁸x(-3)^(-6)x9⁷x(-5)^(-2)x5⁴x1²x6⁰
It might be possible to push this even more but I can't be bothered I've already wasted too long on this lol
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
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.
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)
@@PW-qi1gi What about people born january first 1979?
I think I know a formula for squares.
(x-1 × x-1) = x
x + x-1 = (x-1 × x-1) + x-1 = (x-1 × x) + x = (x × x)
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)
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
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
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
@@kaushalagrawal6258Boi is too young to know
@@pegpin2005 haha thanks! I never did that as a child
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.
Fact 3 is amazing. Thank you Paresh..
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
Or if you will be alive that’s:
0.000000000000001% minimum
Or if you’re healthy
0.000000000001%
That is a very fun and awesome video! Thanks, and Happy 2025 everyone! 🎉
Good video. nice clear explanations as always!
This is perfect; This gotta be a great year
1:52 The only issue with this is 1. I wasn’t born in any of those years 😞, and 2. My mom says I’m not supposed to be floating around in space…
Bruh
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
@@kinkinawesome If a number has 6 factors then it's square is product of proper factors
Take 28 which has factors 1,2,4,7,14,28.
Take product of 2,4,7,14 which is 28^2
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).
The mind behind the facts is amazing. May 2025 be an auspicious year.
That was amazing!
This year is truly fascinating
The next year when facts 2 and 3 will be significant again is a thousand years from now. Amazing!
Amazing!
Happy New Year Presh
Great video Presh Talwalkar
Don't know this much Pattern existed and i think there will be more 😅
But Happy New Year 2025
Very cool video! 😊
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
gg
How did you know that?
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.
I swear, The Hidden Path to Manifesting Financial Power is one of the best books I’ve read. It’s life-changing.
5 years ago, we also had a year that was a mathematical wonder too as 2020 was double 20
It's wonderful
Thanks for the good video
hopefully this is gonna help me in the upcoming math olympiad
yeah, this kind of question comes up in those
Good luck!
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
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........
8:17 the power and their corresponding base adds up to 7 as well 😮😮
This video makes me feel that the year would be good :D
I am watching this at 2 AM and this is what im gonna write on my final exam tommorow
this is quite litterally the perfect year for the number 45
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
Would be interesting to know which next year will have all these properties.
2025 is a special year with a lot of mathematical characteristics.
2025=1⁰+2⁰+3⁰+4⁰+...+2025⁰🤯
2025 = 1¹ + 1² + ... + 1²⁰²⁵
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.
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 like that cubes to squares proof!
fun fact I found myself, for the last one, if you go to 44 instead of 45 you have 1935 which is one digit under 1936 (remember, 44^2) and if you go to 46, you have 2117, which is one digit over 2116 (which is 46^2) !!
That's enough motivation for not wasting this year
perfect!
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 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.
It HAS to be a good year
0:50 Also people born in late 1979 from now until their birthday.
2025- Amazing mathematical year
Excellent
This is too cool. I may be able to live to the next square year of 2116... I'll only be 134.
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
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.
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.
😅😅😊😊😊😊
Wow! All those unusual facts about 2025! What an odd number 😉
I'm aiming for that 2116 date!
I have noticed that 2025 has 13 divisors and 5 divisors 1, 9, 25, 81, and 225 are perfect square numbers.
This is a crazy number
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
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.
Hes also the joe biden of turkish politics
1:47 and 1980 is 90 years apart from 2070, and 90 is 45x2, referencing the 45^2 😮
My being very excited over this proves that I am a nerd. 😂
2025 is my favorite year!
How do you type a square or cube?
This is incredible 😢
Fun fact:
99999999999999980000000000000001
Split in half and add
9999999999999998 + 0000000000000001
=9999999999999999
9999999999999999 power 2
=99999999999999980000000000000001
(The first number)
Same happens with 2025
😊
M, father was born in 1980 and his birthday is in a month so thank you :D
Anyone seen CtC's video about 45²?
I
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.
I can see you are implicitly using "mathematical induction," as ancient Greek mathematicians used to. To be rigorous, you need also to state the base case.
This is like those ILUMINATI CONFIRMED videos but without being illuminati
3:27 Al Khwarizmi would be so jealous
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.
3:58 i was gonna comment that
I was born in 1979 and am 45 most of this year.
2:48 it's a description not a term (called)
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...
And the first two digits of the square are 25 minus the difference between the number and 50, because
(50-x)^2 = 100(25-x) + x^2
so you can mentally compute those squares this way. Also, you can make a similar observation about the squares of 51 through 59.
NGL, that last one 🤯
As an average of 2 cousin primes, whose square is the year:
43*47 = 2021 is only 4 years ago
The other two neighbors:
37*41 = 1517
67*71 = 4757
Twin primes dont even come close to today:
41*43 = 1763
59*61 = 3599
Two more fun facts. The golden ratio is also in there.
Between 2025 and 3025 exactly 1000 years.
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.
cool!
For the first one, 45 years after 45^2 is when you need to be born for you age^2 to be the year
The fifth one is actually the 1st one explained..😂
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
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?
My suggestion: Bifursqum numbers, for Bifurcate then square the sum.
Also the year of the snake
Mathematicians waiting for the year 3025 to upload an other video
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
1:52 hawk 2(ah)
I miss the outro music. When did it stop?
Why did it stop? ??
All the math competitions gonna be using this one for the next 3 years, coz 2026 is 2 * 1023 = 2026 and 2027 is prime.
I was born in 1980. I turned 45 last Saturday.
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.
for some reason i get infinite ads on this video
And President 45 will be re-inaugurated in 2025!!