Didn't happen to come across the powers of ten, did you? They seem to fit the pattern described in the beginning, albeit not the mathematical formula with 3 - sqrt(5)
something that could be related, but even if it isn't is interesting. with a restricted keyboard, i'll define "{}" as taking the square root of a number, do (x+{x^2+1})^n, where x is an integer greater than 4, and n is any number, you will get n repeating digits after the decimal point. so for example, (5+{26})^4=10401.99990...
as x gets larger, the number of repeating digits increases, and the same when x gets smaller, but x=5 is when the number of digits equals n
The first couple of numbers (99,98 etc.) are not even special imo, there are close to 100,1000,10000 etc. and their square roots are therefore close to 10,100,1000 etc..
I just spent an hour working on this... but it's time well spent!
What actually happens is you can write those constants as roots of a quadratic equation, or rather a family of quadratic equations, and if you allow the number to appear deeper in the square root, there will be more constants.
However, some of these additional roots don't give rise to grafting numbers easily! For instance, getting a grafting number from 4970-100*sqrt(2470) will be quite difficult without some programming.
Generally digit patterns don't interest me very much because they are base dependent. There's nothing intrinsically interesting about the number 98 viz a viz its square root if we are talking about digits. 98 in base 5 is still the same value, but the property being explored is no longer applicable. To find something intrinsic about numbers ignore digit patterns, find something which is true regardless of base which is just the system by which the number is being represented.
I programmed a little in python when I was in the 9th grade. Granted, it was a first level programming class that got cut from our school after that year so I didn't learn anything too detailed.
Those reoccurrences of the original numbers are not freak occurrences. Ther are FREQuency occurrences.There is a differencve betwen the sqr rt of 2 and the halvsaa and doubles. When the digit is smaller than 5 the result will be a single digit. Thsi causes a repetitive sequence. This is the same law, which governs exponentation of numbers which are not 10, and having the algorithm, of number,place, and quantity match to break down. (^21 is a 21 digity number. 9^22 power is not a 22.
i laugh at physicists who call biologists stamp collectors...i used to live with 3 post-grad physicists, and when id go to their office in the physics department there were whiteboards with various problems that id solve and get the ire of other physicists in the department, because id always sign off as the stamp collector or the lowly biologist. stamp collecting is fun, and being a plant systematist all i do is 'stamp collecting'...easy job, and i get to look at flowers all day, win-win
Computer programming is like skydiving in that when most people do it for the first time, they spend the entire time screaming.
This video that shows 'recreational mathematics' is phenomenal BTW, I love recreational mathematics stuff. I wish Martin Gardner was still alive so you could do a series of videos with him...
Well, I don't know about higher maths or anything but, if there is an infinite amount of numbers, I think the probability for a random number's square root to contain the number itself is actually pretty high. Of course, this is not me taking away any credit but why is that so special?
I was actually thinking it wouldn't be that hard to write some code for this problem as I usually end up writing some C code myself when I'm looking for patterns.
To be honest I'm more interested how did you end up with 3-sqrt(5). You should do a follow up on that.
@jamma246 He says in the video that he's never seen anyone talk about this before. How could this possibly be why people find maths boring if most mathematicians haven't seen it, let alone people such as yourself?
@knightnicholasd Lots of things in sciences don't seem to have "functions" at the first glance, but that doesn't mean they're useless! Most people thought the internet and computers would be useless when they were first dreamt up!
He focused his energy into learning computer programming because of this, which is going to help in other ways. He's also introducing a new concept to the pure math world, which applied math people will then take as a tool and potentially find it's application. There are many examples where pure math such as topology and number theory have actually found application in nature, so I'm sure somewhere along the line we will find one for this concept.
I would imagine these grafting numbers are a lot more frequent as you lower the BASE. Is their some kind of relationship between the BASE used and the frequency. Now there's a project to keep you busy!
@Adj19888 Try using a calculator with a higher number of places displayed. Until the 10-billionths (10^-10) spot you will only see 9s after the decimal, where you will find a 4.
Surely you missed 77 off this family, which you had as part of a different family earlier? That way you can multiply by 100 for the first step rather than 1000
Reminds me of how people start to look for messages, codes or patterns in the math constants. Especially the "message spotters" are hilarious because though math may be strict, deterministic and completely predictable (given you've found the sequence generating function) our language is completely arbitrary.
I noticed how 3 and 5 are prime so I played around with 5 and 7 and found that the numbers match from the second decimal place of 5-sqrt(7) and the first decimal place of (5-sqrt(7))^2 as far as wolfram alpha allows which is over 3000 decimal places.
@AlphaAndOmeg4 Holy F·$% youre right! i only tried a few cases .....and the non prime pairs seemed to not obey the grafting property until i got to(7- sqrt(37))^2 and (7- sqrt(41))^2, anyway im hooked.
@AlphaAndOmeg4 I notice that 7-sqrt(11) doesn't work. But, I bet if you switched to a higher base, it would (don't have time to check this myself). Eg. start doing the numbers in base 16 and try 7-sqrt(B), B-sqrt(D) etc.
@parkamark base 16 didn't work. But I found that 5-sqrt(x) where x is an integer between 1 and 24 not including 4 and 16 have the same property. After x=25 of course it become negative.
I have recently been on an obsession of infinite tetrations. (Like root 2 to the root 2 to the root 2...) Could you guys PLEASE do a video about them? :)
After watching the video on narcissistic numbers., I had gone to write the program to find those as well. I completely agree that the ability to use basic programming is incredibly helpful to a mathematician. Maybe not so incredibly deep into the language like graphical user interface design., but at least far enough to do logic and loops.
Good morning. You have been in suspension for: 99999 99999.... This courtesy Call is to inform you that all test subjects should vacate the Enrichment Center immediately.
you should do a video on the Laplace transform. it came up in a couple classes, so i had two professors explain it to me, but still the mathematics behind it leaves me with an incredibly blank stare.
My though is that, since the square root of 100 is 10 and the square root of 10000 is 100, and so on... why wouldn't numbers that are in a close proximity to these numbers have a square root that also begins with the numbers in the original number?
Let's say you have (x+e)^2, where x is say 10 and e is a very small number. Then the generated decimals come from (x^2+2ex+e^2) which equals (100+20e+e^2). As "e" gets near zero, the decimals of e^2 are negligible and the generated decimals come from 20e, or even simpler 2e.
So if you wanna double a number, and only have the square function,
take 10 point some zeros, fill in your number, and square it, and you find the number doubled in the decimals.
The starting point is very obvious The square root of 100 is obviously 10, so numbers that approach 100 will approach having a square root exactly 1/10 as big. I do the same sort of thing for fun :D
@supergsx Maybe you can eventually connect any numbers together, but the way you connect them has meaning. Besides, just because they have an infinite number of digits doesn't mean they're random. You're more likely to see some digits than others. They're also derived, unclear patterns from clear ones. It's like aperiodic tilings - You can take a mundane high-dimensional object and tile it, but when you flatten it into 2D, you can get a never-repeating pattern.
@LokiClock You have a good point (and I commented that before watching the rest of the video and hearing about his algorithm), but finding patterns in chaos (such as the digits in irrational numbers) is much like finding patterns in the alignments of the rocks on Mars. Conclusions in that type of data are completely useless.
@supergsx It depends on how well they correspond. If you take another photograph with the same alignments it means nothing, unless you're proposing this is a photograph of the same rocks. If you prove it's a photograph of the rocks on Mars, then it doesn't matter how good the film is, because you can come back later and take a better picture. By virtue, you've proven that no matter how good a picture you take it will continue to look like those rocks, in that alignment.
a) this channel should be named mathematical curiosities, good channel otherwise.
b) so what your saying is that you discovered an underling property of rational numbers as expressed by the decimal system? am quite certain this can be used in cryptography.
Throughout all of these videos, I keep trying to convince myself there is some practical application for these numerical properties. So I think what you mentioned as well as computer security systems.
@numberphile One of my favorite things about the use of the golden ratio would have to be in the formula for the n-th Fibonacci number (derived via linear algebra finding the eigenvalues of the matrix [{1,0}{1,1}]). The original discovery of the number is really fun too (the similar rectangles proof)
@mungorn Here is a better way of presenting it: the golden ratio=(1+sqrt(5))/2 and (3-sqrt(5))/2 ; add both ratios together ,they’ll give you 2 exactly.
i like how the root of 98 = 9.8994949.. and root of 99 = 9.949 shares the exact same digits for the first few places. when you take out the 9.8 in root of 98
I got so excited when I saw the pattern emerging before he mentioned it, then he mentioned it, I cant explain this emotion. Now I want to try it in different bases, would you mind sharing the code you made?
the thing my friends showed me which was awesome is that if you take any number and divide it by 9 for the number of digits, you get the number.
For example:
59 / 99 = 0.5959595959595959
143 / 999 = 0.143143143143
123456789 / 999999999 = 0.123456789123456789123456789
TheGuyInUrCloset 4 hours ago
NEIN! NEIN! NEIN! NEIN!
RBuckminsterFuller 6 hours ago
lol i thought i was on a hitler video for a second..."NINE NINE NINE!!"
nini073210 6 hours ago
Seems to me that we can write this pattern as a rule, sqrt[(4-2φ)*10^(2n-1)] = sqrt(6-2φ)*10^n, where φ is the golden ratio.
ZizooMoDaI 1 day ago
if u take the square root of 100 u get 10.0, grafting number?
treeklimbers 3 days ago 2
if you notice, the second thing he tries, the number before the decimal is the original number plus one
Minjask6572 5 days ago in playlist Uploaded videos
woh
JustinNengelVEVO 5 days ago
Excel??
At least learn Python or something. You're a mathematics professor! Get some real tools.
Not that I'm all that clever, but...
TheGzeus 5 days ago in playlist Uploaded videos
@TheGzeus THIS IS WHAT I GET FOR COMMENTING EARLY.
I'M AN ARSEHOLE.
TheGzeus 5 days ago in playlist Uploaded videos
@TheGzeus lol
JesseDCrespo 3 days ago
@TheGzeus Its the internet, seems to bring out that ass in all of us >.<
perrin275 14 hours ago
It seems to happen near orders of magnitude.
PykohYT 5 days ago
@PykohYT yeah. as long as its close enough to 10, 100, 1000 it works. sqrt100=10,0 so that's why
stuntyannick2 4 days ago
Ernest Rutherford, "All science is either physics or stamp collecting.
ijunkie 5 days ago
root of 100 is 10.0 OMG !!
ternvall 6 days ago
lim n→infinity
sqrt(10^(2n-1)(3-sqrt(5)) = (10^n(5-sqrt(5))
DylanMadisetti 1 week ago
Comment removed
DylanMadisetti 1 week ago
Didn't happen to come across the powers of ten, did you? They seem to fit the pattern described in the beginning, albeit not the mathematical formula with 3 - sqrt(5)
MinecraftPuzzleMaps 1 week ago in playlist Uploaded videos
this is stupid -_-
IcyCylena 1 week ago
@IcyCylena trollolololol?
06Perseus 6 days ago
@IcyCylena Actually, it seems pretty smart...
Pwnzistor 5 days ago
I wrote all this down and showed it to my Algebra teacher, and he thought I was a genius for a while.
SanguineSteel 1 week ago
@SanguineSteel What do you think the result will be if I write the 98, 99, 9998, 9999 one on the board while my Algebra teacher is out of the room?
Freefalldreams 3 days ago
You know so much random shit, lol. You should go on a game show, your a fucking walking tivia book!
Ruzlier 1 week ago
Ugh... every time i try to go to sleep i end up watching numberphile all night instead.
carloldelpizzo 1 week ago in playlist Uploaded videos
ಠ_ಠ wtf is your problem?
WEREWOLFxVSxVAMPIRE 1 week ago
something that could be related, but even if it isn't is interesting. with a restricted keyboard, i'll define "{}" as taking the square root of a number, do (x+{x^2+1})^n, where x is an integer greater than 4, and n is any number, you will get n repeating digits after the decimal point. so for example, (5+{26})^4=10401.99990...
as x gets larger, the number of repeating digits increases, and the same when x gets smaller, but x=5 is when the number of digits equals n
DFTBA10000 1 week ago in playlist Uploaded videos 9
9 is a weird number...
Dardanstarnan 1 week ago
Woot, he uses Python to code. Python for the win.
rinzler304429 2 weeks ago
The first couple of numbers (99,98 etc.) are not even special imo, there are close to 100,1000,10000 etc. and their square roots are therefore close to 10,100,1000 etc..
DelphianSociety 2 weeks ago in playlist Uploaded videos
Astonishing.
normally I hate maths and
English isnt my motherlanguage but I learn more then in my language
2028SM 2 weeks ago
1:05 sounds like inglorious bastards
mattmar96 2 weeks ago
7:50 BLEW MY MIND. HOLY SHIT
harryh111111 3 weeks ago in playlist Uploaded videos
I just spent an hour working on this... but it's time well spent!
What actually happens is you can write those constants as roots of a quadratic equation, or rather a family of quadratic equations, and if you allow the number to appear deeper in the square root, there will be more constants.
However, some of these additional roots don't give rise to grafting numbers easily! For instance, getting a grafting number from 4970-100*sqrt(2470) will be quite difficult without some programming.
unekdoud 3 weeks ago
manycam.com
ljb31218 3 weeks ago
that's cool if you want to rec your desk top or loptop you can download many cam at
ljb31218 3 weeks ago
How the fuck can you remember all those sequences!?
kiemul136 3 weeks ago
@kiemul136
Black magic
rinzler304429 2 weeks ago
Generally digit patterns don't interest me very much because they are base dependent. There's nothing intrinsically interesting about the number 98 viz a viz its square root if we are talking about digits. 98 in base 5 is still the same value, but the property being explored is no longer applicable. To find something intrinsic about numbers ignore digit patterns, find something which is true regardless of base which is just the system by which the number is being represented.
PlasteredDragon 3 weeks ago in playlist Uploaded videos
I programmed a little in python when I was in the 9th grade. Granted, it was a first level programming class that got cut from our school after that year so I didn't learn anything too detailed.
009untitled 3 weeks ago in playlist Uploaded videos
Wait, what o.O
Avistiff 3 weeks ago
Those reoccurrences of the original numbers are not freak occurrences. Ther are FREQuency occurrences.There is a differencve betwen the sqr rt of 2 and the halvsaa and doubles. When the digit is smaller than 5 the result will be a single digit. Thsi causes a repetitive sequence. This is the same law, which governs exponentation of numbers which are not 10, and having the algorithm, of number,place, and quantity match to break down. (^21 is a 21 digity number. 9^22 power is not a 22.
radiowwww 4 weeks ago in playlist Uploaded videos
RE: Your BASE 10 reference. Which BASE number will allow PI to be a repeating number?
markakroll 4 weeks ago
Comment removed
123412343214321 4 weeks ago
The number with the lowest accuracy in the family discussed (or rather, the smallest number) is 8. sqrt(8) = 2.82842712.
1 is also a "grafting number".
zzzdude9 4 weeks ago
he reminds me on marshall from how i met your mother :p
TheRolemodel1337 4 weeks ago in playlist Uploaded videos 3
yay python!
andreirocks1992 1 month ago
i laugh at physicists who call biologists stamp collectors...i used to live with 3 post-grad physicists, and when id go to their office in the physics department there were whiteboards with various problems that id solve and get the ire of other physicists in the department, because id always sign off as the stamp collector or the lowly biologist. stamp collecting is fun, and being a plant systematist all i do is 'stamp collecting'...easy job, and i get to look at flowers all day, win-win
Tryambakam 1 month ago
Computer programming is like skydiving in that when most people do it for the first time, they spend the entire time screaming.
This video that shows 'recreational mathematics' is phenomenal BTW, I love recreational mathematics stuff. I wish Martin Gardner was still alive so you could do a series of videos with him...
otakucode 1 month ago
up until 3:30 i was writing a comment to just make a small program that searches for them for you
mcjohnalds45 1 month ago
Cube Root of 999 is 9.99...., Cube Root of 999999 is 99.9.... etc
CallMeJaayx 1 month ago
i find it fascinating
crater7 1 month ago
this seems more like numerology than mathematics
qtzlctl2012 1 month ago in playlist More videos from numberphile
Well, I don't know about higher maths or anything but, if there is an infinite amount of numbers, I think the probability for a random number's square root to contain the number itself is actually pretty high. Of course, this is not me taking away any credit but why is that so special?
xarepe1 1 month ago
is there a proof for this?
plz reply
lolz2018 1 month ago in playlist Uploaded videos
@lolz2018
The special number he gets in the end is 3-sqrt(5)
It can also be written as 2*(1-1/phi) with phi being the golden ratio ;)
Maybe you could proof that this number emerges from the decimal system and using that the golden ratio is the limit of sqrt(1+sqrt(1+sqrt(1+....)))
But that's just a wild guess :D
deadfr3d 1 month ago
I was actually thinking it wouldn't be that hard to write some code for this problem as I usually end up writing some C code myself when I'm looking for patterns.
To be honest I'm more interested how did you end up with 3-sqrt(5). You should do a follow up on that.
MrIStillDontCare 1 month ago 3
Just out of curiosity, did you employ a regex backreference to identify the roots that matched?
kd1s 1 month ago
This is why people find maths boring.
jamma246 1 month ago
@jamma246 He says in the video that he's never seen anyone talk about this before. How could this possibly be why people find maths boring if most mathematicians haven't seen it, let alone people such as yourself?
olivecronas 1 month ago
8 works too, 2.828427.......
MrTobi48 1 month ago
This has been flagged as spam show
This has absolutely no function. Focus your energy toward something potentially useful!
knightnicholasd 1 month ago
@knightnicholasd like writing comments on YouTube videos to someone you've never met and know nothing about?!
numberphile 1 month ago 51
@knightnicholasd Lots of things in sciences don't seem to have "functions" at the first glance, but that doesn't mean they're useless! Most people thought the internet and computers would be useless when they were first dreamt up!
nipuna666 1 month ago
@knightnicholasd This problem prompted him to learn a programming language. How can learning a programming language not be considered useful?
waynedanielsinclair 1 month ago
@knightnicholasd
He focused his energy into learning computer programming because of this, which is going to help in other ways. He's also introducing a new concept to the pure math world, which applied math people will then take as a tool and potentially find it's application. There are many examples where pure math such as topology and number theory have actually found application in nature, so I'm sure somewhere along the line we will find one for this concept.
vampiracy 4 weeks ago
@knightnicholasd You must be an engineer.
Lyrelia 3 weeks ago
@Lyrelia Big talk from a waitress.
nilbud 3 weeks ago
does anybody know the means by which he found that the number approached 3-sqrt(5)
trongi636 1 month ago in playlist Uploaded videos
I would imagine these grafting numbers are a lot more frequent as you lower the BASE. Is their some kind of relationship between the BASE used and the frequency. Now there's a project to keep you busy!
MelTurpin 1 month ago
@MelTurpin As you decrease the base the no of usable digits decreases.. so its more likely to find repeating patterns...
chaitan94 1 month ago
Looks like top commentors know more then this devoted numberphile
Lolskatorian 1 month ago
999998 is 999.999 not 999998
Adj19888 1 month ago
@Adj19888 Try using a calculator with a higher number of places displayed. Until the 10-billionths (10^-10) spot you will only see 9s after the decimal, where you will find a 4.
PoketoMtg 1 month ago
Also, the resemblance to a Monty Python sketch comes to mind...
eelcodelange 1 month ago
Yeah. Python coding you good sir, win.
headcracker100 1 month ago
Welcome to the Python world, I recommend you to take a look at Numpy!
genstian 1 month ago
This is my favourite numberphile so far. Intriguing start, simple beginning and rabit-hole type depth. Excellent! (Thank you.)
recklessroges 1 month ago
Hitler would like this video. NEIN NEIN NEIN NEIN NEIN NEIN NEIN NEIN NEIN!
RasmusLastname 1 month ago 27
@RasmusLastname ROFL
AtactHD 1 month ago
Python FTW!
pabloso 1 month ago
@pabloso Real men use FORTRAN.
SonOfNye 1 month ago
Surely you missed 77 off this family, which you had as part of a different family earlier? That way you can multiply by 100 for the first step rather than 1000
ChrisEmerson 1 month ago
Or even 8, which would be the first term using your formula (square root 2.8....)
ChrisEmerson 1 month ago
Also, have fun generalizing this idea over higher roots :-P
FHomeBrew 1 month ago
Reminds me of how people start to look for messages, codes or patterns in the math constants. Especially the "message spotters" are hilarious because though math may be strict, deterministic and completely predictable (given you've found the sequence generating function) our language is completely arbitrary.
FHomeBrew 1 month ago
This is beautiful!
Thank you.
rhorcher 1 month ago
@numberphile do a video on the number "42" XD
chriskevini 1 month ago
At first I thought this was David Tennant.
sbergman27 1 month ago
Synchronicity alert. At the exact moment the camera cut to the clock, I looked at the clock on the mantlepiece. Exactly the same time :D
Naddig74 1 month ago
Well now I'm glad I was really into Actionscripting and XML when I was younger. Now I just have to skydive.
nooneisusingthisname 1 month ago
Now that's a great video! :)
ReasonSharp 1 month ago
I'm amazed by the fact that he remembered so much of these numbers.
juricbenjamin23 1 month ago 4
Comment removed
BomberM7 1 month ago
no more such numbers?
well sqrt(100) = 10.0
*ba dum tsss*
Cr42yguy 1 month ago 85
@Cr42yguy I should think that we could simple refer to this as a trivial solution.
SonOfNye 1 month ago
@Cr42yguy I believe he is talking irrational numbers, not perfect squares.
mysteryx294 1 month ago in playlist More videos from numberphile
I noticed how 3 and 5 are prime so I played around with 5 and 7 and found that the numbers match from the second decimal place of 5-sqrt(7) and the first decimal place of (5-sqrt(7))^2 as far as wolfram alpha allows which is over 3000 decimal places.
AlphaAndOmeg4 1 month ago
@AlphaAndOmeg4 Holy F·$% youre right! i only tried a few cases .....and the non prime pairs seemed to not obey the grafting property until i got to(7- sqrt(37))^2 and (7- sqrt(41))^2, anyway im hooked.
urzua8 1 month ago
@AlphaAndOmeg4 I notice that 7-sqrt(11) doesn't work. But, I bet if you switched to a higher base, it would (don't have time to check this myself). Eg. start doing the numbers in base 16 and try 7-sqrt(B), B-sqrt(D) etc.
parkamark 1 month ago
@parkamark base 16 didn't work. But I found that 5-sqrt(x) where x is an integer between 1 and 24 not including 4 and 16 have the same property. After x=25 of course it become negative.
AlphaAndOmeg4 1 month ago
find it strange how he writes numbers and dots. decimal point looks like multiplication. 7 looks like 1.
SebastianMisch 1 month ago
The square root of 100 = 10.0 . I just repeated the numbers.
rjhrjh3 1 month ago
wow!!!! very inspiring ....u got great mind..keep it up.
legendpawan09 1 month ago
I have recently been on an obsession of infinite tetrations. (Like root 2 to the root 2 to the root 2...) Could you guys PLEASE do a video about them? :)
compaq1275 1 month ago
Comment removed
retardedshrimp 1 month ago
This video put me to sleep, keep it coming :P
mcbeastable 1 month ago
After watching the video on narcissistic numbers., I had gone to write the program to find those as well. I completely agree that the ability to use basic programming is incredibly helpful to a mathematician. Maybe not so incredibly deep into the language like graphical user interface design., but at least far enough to do logic and loops.
MorvyJ 1 month ago
I think this is one of the more fascinating videos so far. Keep them coming, @numberphile!
WiVaBo 1 month ago
Oh yeah, I've done this before. :p
WiVaBo 1 month ago
Doesn't 100 work as a graftying number?
Like, 10.0?
itsmanofpopsicle 1 month ago 11
hehe very entertaining :0 though i don't want to become a mathematician, tis still awesome finding patterns like that
therealjordiano 1 month ago
Somebody give this guy a nobel prize.
AlixeTiir 1 month ago
awesome!
mobabur94 1 month ago
I've been doing some manual searching (in excel) for cube grafting-numbers (excluding the obvious, i.e 1, 2, 1000, so on, so far I have:
cuberoot 999 = 9.99666...
cuberoot 1535 = 11.535492...
cuberoot 48570 = 36.48570154...
cuberoot 646409 = 86.4640946...
these are all of them up to 700000, found manually :)
888Xenon 1 month ago 2
Good morning. You have been in suspension for: 99999 99999.... This courtesy Call is to inform you that all test subjects should vacate the Enrichment Center immediately.
MisiaaMichelle 1 month ago 2
Haha! I love the Python plug. I'm doing the facebook hacker cup problems in Python right now. I would also usher anyone to learn it.
Hoerwik 1 month ago
First thing I thought of when you said you used excel was "this would have been way easier and more thorough in python".
kuni45 1 month ago
It's over NINE THOUSAND.
TheMarkoanton 1 month ago
more numbers that work (exactly):
sqrt(100)=10.0,
sqrt(10000)=100.00,
...
Dlpizz 1 month ago
This sounds like what I do on my calculator when I'm bored in class :P
AraoftheFunk 1 month ago
@numberphile Like a mathematical tautology; ?
LukeCoulson 1 month ago
anyone who finds patterns like this is a beast. ur awesome man
phanatadashi 1 month ago
this is severe numberphilia.
retepaskab 1 month ago
he makes numbers so sexy!
wolgreth 1 month ago
is cool.
masluxx 1 month ago
Very interesting! Can't wait for the episode about the golden ratio!
TrelosLikos 1 month ago
Do a video on 142857
technicallyabsurd 1 month ago
one day it can be useful for finding the formula for prime numbers (maybe) :)
GumokCZ 1 month ago
you should do a video on the Laplace transform. it came up in a couple classes, so i had two professors explain it to me, but still the mathematics behind it leaves me with an incredibly blank stare.
dempdawg2001 1 month ago
PYTHON is awkward. Try RUBY.
knugie 1 month ago
@knugie
:O
Blasphemy! Python is less awkward than Ruby!
genericmember1 1 month ago
My though is that, since the square root of 100 is 10 and the square root of 10000 is 100, and so on... why wouldn't numbers that are in a close proximity to these numbers have a square root that also begins with the numbers in the original number?
FatLingon 1 month ago
@FatLingon
Let's say you have (x+e)^2, where x is say 10 and e is a very small number. Then the generated decimals come from (x^2+2ex+e^2) which equals (100+20e+e^2). As "e" gets near zero, the decimals of e^2 are negligible and the generated decimals come from 20e, or even simpler 2e.
So if you wanna double a number, and only have the square function,
take 10 point some zeros, fill in your number, and square it, and you find the number doubled in the decimals.
sleepingeye 1 month ago
I used to be good at math..until I took an arrow to the knee.
breaneainn 1 month ago
The starting point is very obvious The square root of 100 is obviously 10, so numbers that approach 100 will approach having a square root exactly 1/10 as big. I do the same sort of thing for fun :D
AllOtherNamesTaken2 1 month ago 2
Irrational square roots have completely random patterns. Eventually, you can find anything.
supergsx 1 month ago
@supergsx Maybe you can eventually connect any numbers together, but the way you connect them has meaning. Besides, just because they have an infinite number of digits doesn't mean they're random. You're more likely to see some digits than others. They're also derived, unclear patterns from clear ones. It's like aperiodic tilings - You can take a mundane high-dimensional object and tile it, but when you flatten it into 2D, you can get a never-repeating pattern.
LokiClock 1 month ago
@LokiClock You have a good point (and I commented that before watching the rest of the video and hearing about his algorithm), but finding patterns in chaos (such as the digits in irrational numbers) is much like finding patterns in the alignments of the rocks on Mars. Conclusions in that type of data are completely useless.
supergsx 1 month ago
@supergsx It depends on how well they correspond. If you take another photograph with the same alignments it means nothing, unless you're proposing this is a photograph of the same rocks. If you prove it's a photograph of the rocks on Mars, then it doesn't matter how good the film is, because you can come back later and take a better picture. By virtue, you've proven that no matter how good a picture you take it will continue to look like those rocks, in that alignment.
LokiClock 1 month ago
There actually ISN'T a Wikipedia page on Grafting numbers. Just saying...
4jonah 1 month ago
a) this channel should be named mathematical curiosities, good channel otherwise.
b) so what your saying is that you discovered an underling property of rational numbers as expressed by the decimal system? am quite certain this can be used in cryptography.
AlucardNoir 1 month ago
@AlucardNoir
Throughout all of these videos, I keep trying to convince myself there is some practical application for these numerical properties. So I think what you mentioned as well as computer security systems.
4jonah 1 month ago
Brilliant!
TheLawlbreaker 1 month ago
he sure can remember a lot of numbers, awesome vid
managarm1349 1 month ago
Python is my favourite programming language.
SmartestViking 1 month ago
Your number 7 and ur brackets look the same, maybe u should put a line throught the 7 like a F (sorta) and be less confusing and cool :D
Typho0n86 1 month ago
This should have been incredibly boring to watch. Yet it was presented with such enthusiasm, it was completely enjoyable to watch!
Very good video. Upvoted!
By the way, you have one helluva good memory for numbers if you could just write them down from your head.
I wonder if this can be used to break public key cryptography! :D
Azyashi 1 month ago
2-(3-sqrt(5))/2 = golden ratio= 1.6180339887....
Coincidence? I have no idea.
mungorn 1 month ago 24
@mungorn we've got some golden ratio stuff coming soon
numberphile 1 month ago 31
@numberphile Looking forward to it!
SabibabyS 1 month ago
@numberphile One of my favorite things about the use of the golden ratio would have to be in the formula for the n-th Fibonacci number (derived via linear algebra finding the eigenvalues of the matrix [{1,0}{1,1}]). The original discovery of the number is really fun too (the similar rectangles proof)
MorvyJ 1 month ago
@mungorn That's how you calculate the golden ratio. You set up G -1 = 1/G and solve and that's what you get.
AllOtherNamesTaken2 1 month ago
@mungorn that can be found using sequences and series :)
eek0o 1 month ago
@mungorn Here is a better way of presenting it: the golden ratio=(1+sqrt(5))/2 and (3-sqrt(5))/2 ; add both ratios together ,they’ll give you 2 exactly.
wishbagii 1 month ago 2
@mungorn A much quicker way to calculate the golden ratio is:
0.5 + sqrt(1.25) = 1.6180339887498948482045868343656
Gogargoat 1 month ago
@Gogargoat Yes but, theres the 3-sqrt(5) where they talk about in the vid... So there might be a relation with that...
nastymikkel 1 month ago
@mungorn
GoldenRatio = (1 + sqrt(5)) / 2
sleepingeye 1 month ago
@mungorn Or X-1=1/X or x+1=1/x X=1.6180339887... x=0.6180339887... golden ratio is fun..
livedandletdie 1 month ago
i like how the root of 98 = 9.8994949.. and root of 99 = 9.949 shares the exact same digits for the first few places. when you take out the 9.8 in root of 98
vincentleest 1 month ago
Never mind, as he said, thought processes are generally not original....
PeachesAndSkeet 1 month ago
Sq. root 100 is 10.0
lol
PeachesAndSkeet 1 month ago 2
@PeachesAndSkeet lol there you go, you found a complete family of grafting numbers is you keep going (sqrt(10000) etc...) yey
EvilTwinkie15 1 month ago
@EvilTwinkie15 Hahaha I have them memorized too, just like Matt!!
PeachesAndSkeet 1 month ago
What happens when you square root (3 - sqrt(5)) then? :D
PullarBearBear 1 month ago
wouldnt 100 be a grafting number....
casbboy 1 month ago
the numbers... WHAT DO THEY MEAN?
2minutestomammoth 1 month ago
I got so excited when I saw the pattern emerging before he mentioned it, then he mentioned it, I cant explain this emotion. Now I want to try it in different bases, would you mind sharing the code you made?
balisticjoe 1 month ago
When Matt started finding the pattern behind his grafting numbers, I thought to myself, "Damn, this is turning into some Da Vinci Code shit."
heyandy889 1 month ago
python += 1
heyandy889 1 month ago
Yeah, I'm not jumping out of a plane even if I can.
Trichomes503 1 month ago
Does sqrt(100) = 10.0 count? That seems like a family of quite base(ic) grafting numbers to consider.
elfman901 1 month ago 2