In this video we take a look at some fun mathematical coincidences! #math #weird #coincidence #funfacts
Пікірлер: 483
@Kuvina4 ай бұрын
CORRECTION: At 2:29, the identity should say 8pi*k^2, not 8pi^(k^2). ANOTHER CORRECTION: At 1:36 I said the chance of getting 6 of any digit in a row within the first 768 digits is < 0.1%. However, I just ran a simulation (on 10 million 768 digit sequences), and I got 0.68446%. In my opinion a 0.69% chance is still notable enough to be in this video, but it's not quite as rare as I thought. The confusion comes from ambiguity in language. I thought the source meant "the chance that you get at least 1 of these patterns is
@thumbgoblin47164 ай бұрын
twas bangin👍
@jan_Eten4 ай бұрын
pona suli a!
@GoodrichT64 ай бұрын
Kuvina I think you're so cool ily 🥺
@redstowen4 ай бұрын
Relativity ep. 6 when
@JohnDoe-ti2np4 ай бұрын
Fun video! It's worth mentioning that the theta function explanation of Gelfond's constant e^pi is due to Aaron Doman. By the way, dividing an octave into 19ths arguably gives you even better approximations to "nice" intervals. The minor third (6/5), major third (5/4), and major sixth (5/3) are better approximated by 2^(5/19), 2^(6/19), and 2^(14/19) than by 2^(3/12), 2^(4/12), and 2^(9/12), and the perfect fourth (4/3) and perfect fifth (3/2) are approximated by 2^(8/19) and 2^(11/19) almost as well as by 2^(5/12) and 2^(7/12). So close approximation isn't the only reason for the choice of a 12 equal temperament scale.
@FiniteSimpleFox4 ай бұрын
In general the chance of a specific coincidence occurring is very low, however the chance of *some* coincidence occurring is very high
@bluepiston93474 ай бұрын
Almost no one understands this lol
@AdiDK4 ай бұрын
exactly
@pablojuan46794 ай бұрын
Chance of tornado vs chance of disaster
@samylemzaoui22984 ай бұрын
i cant even count the number of times i tried to explain that to someone and failed miserably
@matze97134 ай бұрын
@@samylemzaoui2298the chance that a specific person understands this is very low, but the chance that some person does is high
@notexactlysiev4 ай бұрын
This is only half mathematical, but I like how the ratio of miles to kilometers (1.609344) is close to the golden ratio (1.61803...) This means you can approximately convert those units using the Fibonacci sequence. 2 miles is about 3 km, 3 miles is about 5 km, 5 miles is about 8 km, etc.
@TabooGroundhog4 ай бұрын
Don’t use the beginning tho lol “1 mile is about 1 km”
@pmmeurcatpics4 ай бұрын
That's so cool!
@jongyon7192p4 ай бұрын
And it's convenient bcuz you only ever need to go *up* the sequence, cuz nobody except USA would convert metric back into Oppression Units.
@gudmansal34684 ай бұрын
close enough@@TabooGroundhog
@12Rosen4 ай бұрын
@@jongyon7192pwtf is an oppression unit
@robo30073 ай бұрын
Here's another one. 82,000 is 10100000001010000 in base 2, 11011111001 in base 3, 110001100 in base 4, and 10111000 in base 5. It is predicted to be the largest number to be represented using only 1s and 0s in all four bases and is thought to be a massive coincidence that a number so large even has that property to begin with.
@skysurfer167913 күн бұрын
Wtf bro💀💀💀
@soapdude14 ай бұрын
One that I was waiting to see if you mentioned: 10! seconds = exactly 6 weeks.
@AlexanderWeixelbaumer4 ай бұрын
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 #Six weeks, you can strike * 6 and * 7 to have a day, they multiply to 42 10! / 42 = 10 * 9 *8 * 5 * 4 * 3 * 2 * 1 #Now you strike 2 * 3 * 4 to have an hour, they multiply to 24 10! / 42 / 24 = 10 * 9 * 8 * 5 * 1 #And finally you can strike 10 * 9 * 8 * 5 to get a second, since they multiply to 3600 10! / 42 / 24 / 3600 = 1 So the "magic" is the 6 in six weeks that is left, because you can use the others to make seconds, days and weeks.
@TabooGroundhog4 ай бұрын
That’s SUPER cool that it’s not just close but exactly three Fortnites. Which I guess makes sense since we use highly composite numbers for times, but it’s lucky that weeks are 7 days. I’ll check the rest cause I’m curious 4! = 24 seconds 5! = 2 minutes 6! = 12 minutes 7! = 1 hour and 24 minutes 8! = 11 hours and 12 minutes 9! = 100 hours and 48 minutes 11! = 1 year 13 weeks 6 days
@letMeSayThatInIrish4 ай бұрын
That's lovely and insane!
@petterlarsson72574 ай бұрын
@@TabooGroundhog its spelled fortnight not fortnite
@XplosivDS4 ай бұрын
@@petterlarsson7257 We have been tainted by those 90's
@iaroslav32494 ай бұрын
The first 40 seconds of the video is literally "How to memorize 15 digits of e"
@mbdg68103 ай бұрын
That is pretty cool though.
@n161613 ай бұрын
My dude just causally explained the mathematical basis for music in the middle of this.
@divinemj36503 ай бұрын
honestly quite incredible
@paintspot2 ай бұрын
Kuvina's not a dude, btw. -Paintspot Infez Wasabi!
@n161612 ай бұрын
@@paintspot my girl just casually explained the mathematical basis for music in the middle of this.
@edvinkarlsson9368Ай бұрын
@@paintspotwhat is kusina then? How is kusina not a guy
@parthhooda37134 ай бұрын
Math class initially: 6:40 me: *blinks for a nanosec* 7:40
@ryandupuis58604 ай бұрын
It should also be noted that these situations only occur in base 10, which is a human-based standard. Other bases may have coincidences like these, either more or fewer, though.
@robo30073 ай бұрын
My favourite mathematical coincidence is that if you look at space between e and pi on the number line and mark a point exactly two thirds across, that point is almost exactly the number 3 (3.000489)
@johnbarnhill3864 ай бұрын
It’s worth mentioning that a lot of these coincidences arise because we use base 10. There might be other coincidences in other bases that we don’t know about
@baconheadhair69383 ай бұрын
whatif we use base 1
@smasher_zed8888Ай бұрын
@@baconheadhair6938 base 1 is kinda just tally marks when you dont do the slash for 5 since the number in the base is just the number when you switch digits, for example in base 2 it goes 00, 01, 10, 11 (counting 1 to 4). for base 1, it would be 1, 11, 111, 1111 (counting 1 to 4)
@Skyb0rg4 ай бұрын
The fact that 2^31+1 is prime is one of the most useful coincidences in cryptography, since large primes are needed for the math aspect and modulo multiplication’s runtime is based on the number of 1s digits in binary which is useful for the calculation aspect.
@themathhatter52904 ай бұрын
Surely you mean 2^31-1
@Trying_to_hit_1_sub_no_content4 ай бұрын
@@themathhatter5290yeah
@vishalmishra30464 ай бұрын
Did you mean 2^16+1 (65537) which is the extremely common RSA public key exponent or did you mean 2^31 - 1 ?
@blackmagicprod70394 ай бұрын
2^31 - 1 is not a cryptographically useful prime.
@hhhhhh01752 ай бұрын
2^31 + 1 is divisible by 3
@Yvelluap2 ай бұрын
2:20 i envy your ability to convey this much raw happiness in a single drawing
@brodydrawsstuff4 ай бұрын
Here’s another fun one: 50/49 will spell out the powers of 2, each spaced 2 decimal places apart. (50/49=1.0204081632…)
@CliffSedge-nu5fv4 ай бұрын
...1632653061... aw, shucks. Had to carry the 1 for 128 since it didn't fit in a 2-digit space.
@CliffSedge-nu5fv4 ай бұрын
Can write it as a series of fractions instead: (2/100)^0 + (2/100)^1 + (2/100)^2 + (2/100)^3 + ... = sum_k=0 to infinity (2/100)^k = 50/49 as infinite geometric series.
@brodydrawsstuff4 ай бұрын
Hell yea
@findystonerush93392 ай бұрын
1/96 Will spill out the powers of four: 1/96=0.01041666666666666666... The powers of fours overlap which makes a string of infinite six's
@areadenial2343Ай бұрын
This one is fun! It works because all rational numbers can be constructed from an infinite series, in this case powers of 2. The same is true for 500/499, 5000/4999, and so on, producing larger spaces between powers of two. Eventually, all the powers of two overlap with each other to form a repeating decimal. However, 5/4 is the only one of these numbers which has a terminating decimal representation: 1.25. (Of course, it can also be represented by the repeating decimal 1.249999999...)
@yellowmarkers4 ай бұрын
One thing I like a bit more than the fact that π has a string of six 9s at digit 763 is the fact that 2π has a string of seven 9s at digit 837. It isn't the first instance of four characters in a row in 2π's decimal expansion (since there was a "1111" before it) but it's still the first instance of five, six, and seven characters in a row.
@DavidSartor04 ай бұрын
Yay.
@asheep77973 ай бұрын
…49999998… turns into …99999996…
@Dissimulate3 ай бұрын
I see average people being surprised by coincidences. I try to explain to them how with the number of things that they see, these coincidences are almost certain.
@PlantNocturnal4 ай бұрын
The fun thing about this is that It's genuinely confusing whether a mathematical coincidence is a thing that makes sense. You have situations like these where there isn't a clear explanation and doesn't seem like there should be, but then everything is still logically determined and interrelated, to some extent just determining that some weird correlation is going on is an explanation.
@fahrenheit21014 ай бұрын
No, most of the times there's no reason at all to find it suspicious Most of these are base 10 specific for example, but there's nothing special about 10 at all.
@petachad84634 ай бұрын
7:30 Woah Woah Woah, the what now? shi went from playing with numbers to hyperdimentional spheres real quick
@axbs48634 ай бұрын
the next 6 digits of e are 235 and 360, being the first 3 prime numbers and the angle of a full rotation lol
@taltalim61744 ай бұрын
it's fascinating how e contains a lot of important math numbers so early, like that gotta be like 1 in a big number and other irrational numbers don't have this "property"
@leave-a-comment-at-the-door4 ай бұрын
@@taltalim6174 wdym other irrational numbers don't have this property? no matter what random sequence of digits you pick, if you stare at it long enough you will find neat patterns and coincidences in it. the number of 'important math numbers' is large enough that you can always find things.
@PantheraLeo044 ай бұрын
There's probably a explanation for why this is the case, but I find it interesting that the first 2 hyper-operations are both commutative and associative but all the following hyper-operations have neither property.
@jursamaj4 ай бұрын
*commutative
@PantheraLeo044 ай бұрын
@@jursamaj thanks
@kikivoorburg4 ай бұрын
I’m a big fan of the Kibi-prefix system. Having ambiguity about numbers is basically always a recipe for some sort of disaster
@xymaryai82834 ай бұрын
i'm always sad that we don't have a 2^x counting system, but the kibi prefix system makes me happy everytime i see it
@mushroomcraft4 ай бұрын
"kibibyte" sounds so stupid, I hate that the power of 10 units even exist, because the way that I see it, they are just a way for drive manufacturers to sell you less storage.
@ZachAttack60894 ай бұрын
@@xymaryai8283If only base-16 was the standard for regular math 😔
@vishalmishra30464 ай бұрын
@@ZachAttack6089 It would be nice if human chromosomes and DNA ensured 8 + 8 = 16 fingers/thumbs in human hands instead of 10 that led to decimal system of numbers.
@ZachAttack60894 ай бұрын
@@vishalmishra3046 Exactly haha. Or 4 on each, like most animals, so that it would be base 8 (which would still work with computers).
@2003LN64 ай бұрын
kuvina is honestly the one person carrying the entire internet's faith, love, and good now
@FZs14 ай бұрын
My favorite coincidence is that the sines of the most commonly used angles (0°, 30°, 45°, 60°, 90°) follow a pattern: sin(0°) = 0 = sqrt(0)/2 sin(30°) = 1/2 = sqrt(1)/2 sin(45°) = sqrt(2)/2 sin(60°) = sqrt(3)/2 sin(90°) = 1 = sqrt(4)/2 This doesn't work for any other value though. Despite that, this is how I always memorized them in school (the cosines are the same but the other way around, because cos(x) = sin(90°-x), and tangents are just sin/cos).
@tobysuren4 ай бұрын
my favourite too, for the sole reason that it's actually useful.
@jursamaj4 ай бұрын
For a given definition of "important"…
@dryden_drawing4 ай бұрын
So glad I scrolled one more down in the comments, I still don't have these memorized and I am starting to really need them
@baldability4 ай бұрын
@@jursamajthese are definitely the most important angles up to 90 degrees in trig
@Shyguy51044 ай бұрын
this is less of a coincidence and more the greeks specifically designed it to be like that for 360 degrees
@pinkraven44023 ай бұрын
As an amateur musician it always fascinated me how actually lucky it is that 12 tone equal temperament (where each note is the previous one multiplied by 2^(1/12) can get you so close to the most important musical intervals such as 3/4 and 2/3. Sure, maybe that's not as surprising, because from all the possible reasonable divisions of an octave, like 13, 14, 15 notes, one of them should be good enough in approximating these crucial intervals, but, idk, it's very pleasing to me
@Relkond4 ай бұрын
2 points about the 7th US president - he was elected in 1828, and served 2 terms. If you draw a diagonal line across his square picture, you get a triangle with 3 angles: 45, 90, and 45 rewriting all that: 2. 7 1828 1828 45 90 45
@lumipakkanen35104 ай бұрын
To truly answer "why 12 notes" you need to consider more than 3/2 and 4/3. One component is to make sure that approximations to 10/9 and 9/8 coincide into a "meantone" which might as well give you 31 notes per octave. Another component is to make sure that three approximate 5/4 major thirds stack up to an octave (in other words tempered 125/64 and 128/64 sound alike) . 12-tone equal temperament is the only equal division of the octave satisfying both of these requirements.
@jhgvvetyjj65894 ай бұрын
The three major thirds stacking to an octave isn’t that important to most music, it’s something that 12edo happened to have, but it’s also related to the 1024≈1000 approximation.
@lumipakkanen35104 ай бұрын
@@jhgvvetyjj6589 yep. 19-tone equal tone temperament also has that 10/9 ~ 9/8, with a ton of other flavor on top of it.
@jhgvvetyjj65894 ай бұрын
@@lumipakkanen3510 12 notes per octave however was a better fit for the Pythagorean tuning, which is based on exact prime factors of 2 and 3. And meantone happened to be the most natural way to incorporate the next prime factor (5) in the 12 tone system, where 5 is approximated as +4 fifths (factors of 3) in the circle of fifths (5≈3⁴÷2⁴). The other possible approximation, 5≈3⁻⁸×2¹⁵ was not as commonly available in a 12 tone keyboard and is not part of a major or minor scale without wolf fifths.
@lumipakkanen35104 ай бұрын
@@jhgvvetyjj6589 Sure, but in that case just say that 531441/524288 is tempered out in the 2.3 subgroup and you're done. No need to involve prime 5. Personally I might even go as far as to interprete 12-TET in 2.3.19 tempering out 513/512 and 729/722.
@jhgvvetyjj65894 ай бұрын
@@lumipakkanen3510 531441/524288 being tempered out is what was mentioned in the video after all.
@UltiMaker24 ай бұрын
Recently there were new SI prefixes. "ronna" means 10 to the 27th, "ronto" is 10 to the negative 27, "quetta" is 10 to the 30, and "quecto" is 10 to the negative 30. This also applies to 5:59, where "quettabyte" (QB) means 10 to the 30 bytes and "quettibyte" (?) (QiB) means 1024 to the 10th power (about 1.267651e30).
@LeoStaley4 ай бұрын
I like the coincidences of the ALMOST kind. Near Miss Johnson Solids are really fascinating. They're ALMOST Johnson solids, but are just SLIGHTLY irregular.
@themathhatter52904 ай бұрын
Other mathematical coincidences involving pi: sqrt(2)+sqrt(3) ~~ pi 9/5+sqrt(9/5) ~~ pi e^(pi*sqrt(163)) ~~ (640320)^3+744 Not involving exact mathematical numbers (mile*Astronomical unit)/(inch*light year) ~~ 1
@aioia38854 ай бұрын
if you ever want to approximate pi with ruler and compass you can draw a circle with r = 1 and then the side length of the inscribed square will be √2 and the side length of the inscribed equilateral triangle will be √3 so if you add them you can approximate pi since √2+√3 ≈ π
@mykal47794 ай бұрын
i feel like a cooler way to phrase the last one is "a mile is to a lightyear as an inch is to an AU" or "there are as many miles in a lightyear as there are inches in an AU"
@ixion2001kx764 ай бұрын
Holy cow, the last one is good to 2.8 parts per Nonilion (10^30)
@ixion2001kx764 ай бұрын
The 9/5ths is good to 15ppm-much better than 355/113
@Anonymous_MC4 ай бұрын
why am i seeing the number 640320 everywhere
@alansmithee4194 ай бұрын
While I don't think it meets the definition of a "coincidence" as provided in this video, something I find really cool is that numbers of the form 1/(99...)8 where you have any number of 9s can display the powers of 2 in their decimal expansions. With m 9s you will get m+1 digits of space for each number. 1/998 gives 0.001 002 004 008 016 032 064 128 256 513 failing at the last digit here because the next number (1024) exceeds the space each number has and adds a one to the previous number, 512. Now 1/8=0.125 which may not seem to follow this pattern, but it turns out the infinite series: sum(n=0 to inf) 2^n/10^(n+1) = 1/8 (0.1+0.02+0.004+0.0008+0.00016+...) generally with m 9s: 1/(999...)8 = sum(n=0 to inf) 2^n/10^((m+1)*(n+1)) There may be better ways of displaying the infinite sums here. Also 1/(999...)7 gives powers of 3, 1/(999...)6 powers of 4 etc. Pretty cool.
@paulamarina044 ай бұрын
5:26 specifically its why we have 12TET (12-tone equal temperament). other tuning systems had existed long before 12TET, which were more focused on having neat ratios between the frequencies of the notes than in having them be logarithmically equidistant from one another. the cool coincidence is that they were /almost/ logarithmically equidistant from one another, which allowed 12TET to be used as a more consistent tuning system cool video!!!
@stevosteffano55774 ай бұрын
Some old favourites, and several new ones. Great video!
@RaichuKFM4 ай бұрын
This was a really fun video! It was nice how you brought up some fun coincidences and what is and isn't actually unlikely about them; a lot of stuff falls prey to overstating that because of a naive view about expectations. My favorite part was the almost 20 + pi result, and the look at the sum that led into. Really cool!
@DissonantSynth4 ай бұрын
Love your channel and videos so much. Super high quality, incredibly interesting, and well explained. Also, there's a modesty / sincerity to your videos, which is very special, because I think you are truly creating and sharing these videos purely for your love and appreciation of math, science, and art.
@Kuvina4 ай бұрын
Thank you so much! That is a very well thought out comment and I really appreciate it!
@Metal_Master_YT4 ай бұрын
@@Kuvina you guys have matching profile pictures!
@Mask60YT3 ай бұрын
my favourite mathmatical "coincidence" is that to get the derivative, you just subtract 1 from the power and multiply by the power.
@user-nu9ol8hv9c3 ай бұрын
how is that a coincidence how else would you find the gradient of tangent
@Mask60YT3 ай бұрын
@@user-nu9ol8hv9c its a coincidence because that is not how the derivative formula was found, it was found using another formula that and coincidentally you can just simply do nx^n-1.
@NidhishwarReddy4 ай бұрын
2:32 it was at this moment my brain.exe stopped working and now i am ded
@lythd4 ай бұрын
a sidenote about the MB vs MiB etc differences, the original definition was that KB MB GB etc used powers of 1024, however it was changed to be consistent with si prefixes, and the new KiB MiB took its place. for legacy compatibility reasons windows keeps using the old definition even though its no longer correct. linux and mac, as well as a lot of programs, use the newer definition of KB/MB/GB or use KiB/MiB/GiB. so it isn't a case of MB being ambiguous, and MiB being strictly defined, its a case of the old definitions still having hold over, and sometimes still being incorrectly taught or used especially with a lack of awareness.
@TheWandererOfDreams3 ай бұрын
That "bye" at the end was so ZESTY.
@joeyhardin59034 ай бұрын
Regarding the one about 2^(7/12) being close to 3/2, I'm pretty sure that's not a coincidence. I've been researching the maths behind 12 tone equal temperament in music for a while now, and actually this property of 12, of being able to approximate lots of rational numbers when in an exponent, is not unique and actually is related to the properties of the golden ratio
@bennett22014 ай бұрын
wonderful video kuvina!! i loved the chords you made for 12th roots of 2!!
@Xonatron4 ай бұрын
4:47 - Explains 12 notes per octave - Very cool. 2:1 or 100% pitch increase (double) is an octave up. Why the same keys resonate perfectly. The 3:2 or 50% pitch increase is called a power chord and resonate the next best. Then the 4:3 or 33.3% is next best. Captured well with 12 notes!
@rafakordaczek32753 ай бұрын
Im so glad that youtube recommeded me this video. I discovered your series on relativity. Your animations are basic, but they are sufficient in explaining any concept. Keep up the good work, and I will see you when you pass 100k subscribers!
@mkwilson13944 ай бұрын
I really enjoyed this, and I didn't expect a stack of 4ths to show up, so even better!
@Metal_Master_YT4 ай бұрын
Why hasn't anyone made a video like this until now? its was a great idea!
@kayleighlehrman95662 ай бұрын
The real coincidence was the maths we learned along the way
@TheArtOfBeingANerd4 ай бұрын
I saw 2^(integer)/12 and immediately thought of music theory. Confirmed when I saw it was aprox 3/2
@FaranAiki4 ай бұрын
Me too, but reversed. I was like... 3/2 and 4/3? Seems like a perfect fifth or fourth or something and then I realized it was 2^... haha
@wuketuke66014 ай бұрын
The end of this video just ruthlessly escelates
@The_Commandblock4 ай бұрын
12, 1 *3, 14, 15* , 16, 17
@TheSheep13 ай бұрын
1:22 hehe 6 9’s
@mikemac81592 ай бұрын
this video has both comforted me and put my brain into a number-obsessed mode thank you very much :3
@MathFromAlphaToOmega3 ай бұрын
I just stumbled across this video, and was shocked to see that theta function identity I mentioned a few months ago on a Mathologer video! One of my other favorite not-quite-coincidences is that e^(pi*sqrt(163)) is nearly an integer. It's related to lots of interesting number theory, like elliptic curves, unique factorization, Euler's prime generating polynomial x^2+x+41, and the Ulam spiral. I'm looking forward to watching more of your math videos!
@Kuvina3 ай бұрын
Thank you so much! Number theory is so cool even though I don't know that much about it. Do you know if that's also related to 163/ln(163)?
@MathFromAlphaToOmega3 ай бұрын
@@Kuvina That's really interesting - I hadn't seen that before. I looked it up and it seems like that one really is pure coincidence. There are a few other small values of n for which e^(pi*sqrt(n)) is almost an integer, like 43, but 43/ln(43) isn't close to an integer. Maybe there is some kind of algebraic "explanation" for 163/ln(163), but it's unlikely to be related to the other number theory properties of 163.
@loftyTHEOWNER4 ай бұрын
The leech lattice could be really useful to create my input vectors to randomly associate them to an output and train the model in a supervised way...
@theodriggers5492 ай бұрын
For the e memorization thing, next is the first three primes (235) and degrees in a circle (360)
@parthhooda37134 ай бұрын
3.14159 is also a coincidence as we have very less chance that random 6 digits are 314159
@amichayr34184 ай бұрын
This is like math asmr. I love this
@ouroya4 ай бұрын
the reason we have 12 notes in an octave is much more historical than mathematical, though it is intuitive to choose an octave (×2) rather than a tritave (×3) or anything higher. the western 12-tone equal temperament tuning has only been in use since around the mid-1580s at the very earliest. there are a lot more tunings out there based on things other than the twelfth root of two for 12-tone octave subdivision that have been around a lot longer, all with different benefits and drawbacks, though 12TET became standardized as it allowed things in any key to sound equal with the same tuning, whereas most other tuning systems result in needing to retune to the specific key of a piece or different keys having different qualities.
@jaroel4 ай бұрын
π^2 is almost the gravitational acceleration with 9.81 m/s^2
@matthewtallent82964 ай бұрын
It's like a massage for my brain ☺
@eriksteffahn61724 ай бұрын
Another interesting consequence of 2^10 ≈ 10^3 is that 2 ≈ 10^0.3. With this you get nice approximations for 10^0.1, 10^0.2, ... based on powers of 2 and 5: 1, 1.25, 1.6, 2, 2.5, 3.2, 4, 5, 6.25, 8, 10 this can be useful to approximate non-integer powers (in particular roots) without a calculator, for example: 5000^1.2 ≈ 10^(3.7 * 1.2) = 10^4.44, which is between 25000 and 32000, so 5000^1.2 ≈ 28000 (correct result is 27464).
@benclancy894 ай бұрын
Love the videos! keep them coming!
@FunctionallyLiteratePerson4 ай бұрын
Always love a Kuvina video 😊
@TheGamingPlanet_4 ай бұрын
MIND. BLOWN
@unflexian4 ай бұрын
hey there's an error in the sound at 5:13, you seem to have forgotten the flats when playing it (played C F B E A instead of C F Bb Eb Ab), making the interval from F to B a tritone instead of a fourth. this does not at all detract from the video quality, best esomath video ive seen since the cursed units video, but just fyi.
@Kuvina4 ай бұрын
Thank you for letting me know! I think I originally had it in a different key and then I moved it down to start at C and wrongfully assumed there wouldn't be any sharps or flats!
@unflexian4 ай бұрын
@@Kuvina ohh i see, well at least now you have a segway into a video about equal temperament or harmony or something if you desire :)
@Leadvest4 ай бұрын
Another great video!
@GuyMonochrome3 ай бұрын
Musician here! 4:49 While it's true that we tune many Western instruments to powers of 1/12, it did not cause us to have 12 notes. Long story short, we call this "Equal Temperament" tuning, which is actually quite new. Other systems were used in the past, such as what Pythagorean used. It had 12 notes, but you could argue that the note F# was tuned wildly differently from Gb, so you could say they were separate notes. Other systems evolved, such as Just Intonation, which adopted the "12" notes from Pythagorean tuning. Interested? Search up 12 TET, 17 TET, and 31 TET.
@ckq24 күн бұрын
Hey I discovered a new coincidence that relates e to pi: The solution to x^x*(1-x)^(1-x) = 0.5^0.5 (See A102268 on the OEIS) x=0.889972 is almost nearly pi^2/16/ln(2) = 0.889927 the number pi^2/16/ln(2) didn't come out of nowhere either, it represents the ratio between (arcsin(sqrt(1))-arcsin(sqrt(0.5)))^2 and ln(1)-ln(0.5). For context on the y(x) = arcsin(sqrt(x)) function, it is the integral of 1/sqrt(x(1-x)), so it maps the numbers from 0 to 1 on a scale that is proportional to the standard deviation to account for the fact that there's a bigger difference between 0.99 and 1.00 than 0.50 and 0.51
@xenmaifirebringer5524 ай бұрын
I personally like how e/π is very close to (√3)/2, the value of cos(30°).
@24spitfire3 ай бұрын
i have been trying to tell a the 22/7 is closer one to everyone for ages
@guigui02464 ай бұрын
I realized that : - In 1 dimension you need 1 support point to not fall (you can't need 0 but there is no down) - In 2 dimensions you need 2 support points to not fall /\ (like a card castle) - In 3 dimensions you need 3 support points to not fall /|\ (like stools have) Does that mean in n dimension you need n support points even if gravity only takes act in 1 of them ?
@user-ef8kc4rv7n4 ай бұрын
I can't find a source for this, but I would guess so because you need n points to define a hyperplane in R^n
@user-ef8kc4rv7n4 ай бұрын
I have the outline of a proof, don't want to do the whole thing. Show a congruence between a vector space of dim n-1 and the hyperplane created by taking weighted averages of n points Show that equilibrium under gravity is equivalent to a projection from centre of gravity in direction of attraction intersecting a weighted average of supports Show that for a stable equilibrium, the same must be true for all points in some ball around centre of gravity, ie true for a nudge in n-1 dimensions (not affected by direction of gravity) Hence a vector space with at least n-1 dimensions in required so n support points are needed This shows no fewer than n work but to show n works, show that the (n-1)-simplex can be arbitrarily scaled to cover the projection of any n ball
@b.clarenc95174 ай бұрын
You are right. It also leads to the following puzzle you can ask around: Why is a 3-leg stool always stable, but a chair never is? Because we live in a 3D world.
@leave-a-comment-at-the-door4 ай бұрын
yes, n fixed points will fully determine a system in n dimensions. if you want to think about why, it's easiest to invoke linear algebra: think of rows as dimensions and colums as your points, so a square matrix with a non-zero determinant will be well-defined.
@hypercoder-gaming2 ай бұрын
Also noteworthy is 13,14,15. If you take just the 3 from 13, it's 31415 which are the first few digits of pi.
@gary.h.turner4 ай бұрын
4:41 - Actually, pi has a "continued fraction pattern" too: π = 4 + {1/[1+X]}, where X is the continued fraction (a0)^2/{2+[(a1)^2/(2+…)]}, and an = 2n+1. This arises from the continued fraction for the inverse tangent and the fact that tan^(-1)[1] = π/4.
@TheBalthassar2 ай бұрын
Here's a weird coincidence, I only just now watched this video, after completely missing it when it released. And both this video and the new one care about 70.
@lilyyy4114 ай бұрын
wake up babe! new video from the nerdy enby is here!
@leave-a-comment-at-the-door4 ай бұрын
someone prob already mentioned this but xkcd 1047: approximations is very relevant here. I'll include it here, removing the jokes: Relation: Accurate to within: One light-year(m) 99^8 one part in 40 Earth Surface(m2) 69^8 one part in 130 Oceans volume(m3) 9^19 one part in 70 Seconds in a year 75^4 one part in 400 π*10^7 one part in 220 Age of the universe (seconds) 15^15 one part in 70 Plancks constant 1/(30^π^e) one part in 110 Fundamental charge 3/(14 * π^π^π) one part in 500 Electron rest energy (joules) e/7^16 one part in 1000 Light-year(miles) 2^(42.42) one part in 1000 sin(60°) = √3/2 e/π one part in 1000 √3 2e/π one part in 1000 γ(Eulers gamma constant) 1/√3 one part in 4000 Feet in a meter 5/(e√π) one part in 4000 (note: taking the e-th root of pi is very cursed) √5 2/e + 3/2 one part in 7000 Avogadros number 69^π^√5 one part in 25,000 Gravitational constant G 1 / e^(π - 1)^(π + 1) one part in 25,000 R (gas constant) (e+1)*√5 one part in 50,000 Proton-electron mass ratio 6*π^5 one part in 50,000 Σ 1/n^n from 1 to ∞ ln(3)^e one part in 100,000 √2 3/5 + π/(7-π) one part in 220,000 Liters in a gallon 3 + π/4 one part in 500,000 g 6 + ln(45) one part in 750,000 Proton-electron mass ratio (e^8 - 10) / ϕ one part in 5,000,000 Ruby laser wavelength 1 / (1200^2) [within actual variation] Mean Earth Radius 5^8*6*e [within actual variation] γ(Eulers gamma constant) e/34 + e/5 one part in 2,000,000 √5 (13 + 4π) / (24 - 4π) one part in 13,000,000 (he had a joke about 1/137 but I was curious if I could find anything. sadly nothing interesting, but here's the attempt): Fine structure constant 1/137 one part in 3,800 1/137.036 one part in 150,000,000 (actual inverse is 137.035999084...) 1000/((5^2+π)^2-1)^√π one part in 120,000,000 averaging those two gets you one part in 1,400,000,000 attempt 2: 1/ (100* (4√5−1÷8) ) one part in 100,000
@QP92374 ай бұрын
Saw Gelfond's constant (my favorite number) in the thumbnail and knew I had to watch the video 😂
@EPMTUNES4 ай бұрын
very cool video!!!
@revimfadli46664 ай бұрын
Is this the math equivalent of "names alike" memes?
@Jemmysponz14 ай бұрын
very cool video, thank you!
@glowstonelovepad92943 ай бұрын
If you divide or multiply pi by 2, there will be 7 9s in a row there because the 6 9s have 4 before them and 8 after them.
@jursamaj4 ай бұрын
0:54 Regarding these criteria: try representing numbers in other bases. You'll find these coincidences disappear… while others appear.
@mofekayode89444 ай бұрын
awesome video!
@OwenGalaxyАй бұрын
I came from that other video that ripped off your video - yours is much better.
@puzzleticky84274 ай бұрын
This is what mathematicians like about maths
@diegovasquez8404 ай бұрын
My favorite is from physics, where pi^2 is very close to the gravity constant for earth in meters per second
@caspermadlener41914 ай бұрын
The Leech lattice indeed has a cool construction using its Weyl vector, but the even unimodular lattice in 8 dimensions does not have this construction (although the construction for this lattice is way simpler). It is a bit of a coincidence, also 1 is a cannonball number as well.
@morgan04 ай бұрын
i don’t remember any specifics rn but i remember being fascinated by repeated multiples of some N in the digits of a number divided by that N, i think mainly 7 but also possibly others, maybe it has to be coprime to the base
@lunaros42093 ай бұрын
Is the string piece in the intro the first half of Iceland from the "Musical Map of Europe" video? I thought I recognized those notes.
@aniruddhvasishta83344 ай бұрын
I'm sure that you could find tons more coincidences if some of these equations were written in a base other than decimal.
@lodewijk.4 ай бұрын
babe wake up new kuvina video dropped
@norude4 ай бұрын
Wow, I thought it would be some person, far from math explaining, how 13 is the devils number because of some coincidence, but it was really interesting, especially the last cannon-ball part
@rociochave1066Ай бұрын
I just realized... e has the exact digits of pi just scrambled.........
@paulcastelein14053 ай бұрын
I belive that the kilobyte idea comes from the binary system. Since computers use base 2 some people decided to use base 2 for their bases, and 2^10=1024, however some other people decided they'd rather use the base 10 system as it is the one we typically use and they changed the units accordingly, this makes it different to coordinate
@berghwilliam4 ай бұрын
Not really a coincidence but the square root of 2 added with the square root of 3 is almost pi.
@norude4 ай бұрын
1828 is the birth year of a famous Russian poet Alexander Pushkin.
@FlorissMusic4 ай бұрын
you just explained twelve tone equal temperament in a way that it clicked for me… and it’s not even a music theory video, mind blown
@robo30073 ай бұрын
240 has its digits arranged in descending order in base 2, base 3 and in base 4.
@user-qv5wl7wq1t4 ай бұрын
Imagine if every digit of e had a pattern
@nanamacapagal83424 ай бұрын
Some more coincidences (and explanations): The 3² + 4² = 5² and 10² + 11² + 12² = 13² + 14² are part of an infinite family of these sums: 21² + 22² + 23² + 24² = 25² + 26² + 27² Where the largest term on the left is exactly 4 * a triangular number. This even works in 1st powers (for 2 * a triangular number) 1¹ + 2¹ = 3¹ 4¹ + 5¹ + 6¹ = 7¹ + 8¹ 9¹ + 10¹ + 11¹ + 12¹ = 13¹ + 14¹ + 15¹ As well as 3rd (6 * a triangular number) and 4th (8 * a triangular number) powers, though with slight modification... 5³ + 6³ + 2(1³) = 7³ 16³ + 17³ + 18³ + 2(1³ + 2³) = 19³ + 20³ 33³ + 34³ + 35³ + 36³ + 2(1³ + 2³ + 3³) = 37³ + 38³ + 39³ 7⁴ + 8⁴ + (8/2)³ = 9⁴ 22⁴ + 23⁴ + 24⁴ + (24/2)³ = 25⁴ + 26⁴ 45⁴ + 46⁴ + 47⁴ + 48⁴ + (48/2)³ = 49⁴ + 50⁴ + 51⁴ There's a great explanation of these on Mathologer, and the comments may leave some insight about the higher powers. sqrt(2) + sqrt(3) ≈ pi. This one comes from two different approximations of pi. Start with a circle of radius 1. Its circumference should be 2pi. If you inscribe a square in the circle, its perimeter should be 4sqrt(2), meaning pi is about 2sqrt(2). If you circumscribe a hexagon outside the circle, the circumference should be 4sqrt(3), meaning pi is about 2sqrt(3). If 2sqrt(2) is an underestimate, and 2sqrt(3) is an overestimate, then the average should come pretty close, and indeed it is. Thus, sqrt(2) + sqrt(3) ≈ pi.
@mujahid.63723 ай бұрын
This video made my day
@lawrencejelsma81184 ай бұрын
It is accidental. By the way ... The approximation of exact real values such as e^π = 20 + π is of the form e^x = (1)(x + 20) where the Lambert W function solves for x. It might approximate to π (checking in Wolfram Alpha online calculator) with sufficient error minumal in significant digits truncated and rounded, etc.