What is the area of a Squircle?
Vložit
- čas přidán 22. 05. 2024
- Check out www.kiwico.com/standupmaths and get 50% off your first month of any crate! Maybe enjoy making a pencil sharpener! Not that I'd know what that's like...
This is the GeoGebra file Sam Hartburn made for me:
www.geogebra.org/m/pffgbck8
Here is The Coding Train's first part of the Super Shape series.
• Coding Challenge #19: ...
I mentioned the these old videos of mine:
Ellipses and perimeters • Why is there no equati...
Generalising fibonacci • Complex Fibonacci Numb...
Lemniscate on MathWorld
mathworld.wolfram.com/Lemnisc...
This is a really good write-up about Gauss and the Arithmetic-Geometric Mean.
homepage.univie.ac.at/tomack....
This is a nice related problem about the area v perimeter of a squircle.
www.johndcook.com/blog/2019/0...
Cheers to my Patreon supporters for whom I have dedicated one digit of Gauss's constant each. It was their inspiration who made me do the 'multiple Matts' thing. You can also help support and shape the videos I make! / standupmaths
CORRECTIONS
- If you feel a sense of déjà vu: yes, the two sections at 16:13 and 16:45 cover the same content. I tried saying it two different ways and we accidentally left both in the edit. So, let's call that 'buy one get one free' sale on learning.
- At 21:42 I say "geometric mean" instead of "arithmetic mean". And that is probably not the only time. These words have lost all meaning to me.
- The Patreon credits stop early! Long story. I'll explain on Patreon.
- Let me know if you spot any other mistakes.
Crazy amount of editing and meshing of footage by Alex Genn-Bash
Maths graphics by Sam Hartburn and Matt Parker
Kitchen by Carrie and Nina
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b... - Zábava
![General Relativity: Top 05 Mishaps [inc INTERSTELLAR]](http://i.ytimg.com/vi/Z4oy6mnkyW4/mqdefault.jpg)
Sorry the Patreon credits cut off! They are all here czcams.com/video/s7YOx_3qTJc/video.html so you can find your Gauss digit. Or, here, just take this one: 8
And thanks to KiwiCo for supporting me along with every other nerdy channel. Best use my link just to be safe: www.kiwico.com/standupmaths
Square + circle is a square circle
10:32 Can't Lemniscate rhyme with "sideways eight"?
Assuming the biscuit-segment was filmed in your own kitchen, did your wife give any looks or come with snarky remarks about the ordeal?
11:07 Nevermind. I see it's far to late to pronounce it Lemniscate, as script and video are all done by this date. But to other who now consider this debate, that sideways eight can be placed on a plate and you'd be rhyming in no time; there'd be no need to wait. *Sigh* but still late for this video, such is it's fate.
G'night
He has done it, he has officially achieved both quality and quantity.
Yeah, three Matts. That's quantity.
@@vigilantcosmicpenguin8721 Lmao, I didn't intend it (as I posted it before watching the video), but it's so fitting.
Love your channel bro, wish mine was as good!
+
@Amelia Kamel🌹 bot
Matt is the only person I know who can successfully bully himself.
I see this is someone who doesn't have Anxiety and/or Depression
i dunno... have you seen how weezywaiter treats his clones?
and have us picking sides. Legitamately had to remind myself that they are all the same person when Matt 2 and Future Matt were doing all of the work :P
Ryan Reynolds dose it too
I see you haven't discovered Ryan George
I’m 20 years old with an A level in further maths and thinking “the value of pi for a square is 4” kinda just blew my mind.
It's sometimes said by players of games on square-grid boards with diagonal movement "This is the kind of wonkiness you can expect from a world where pi equals 4."
@@alexnobody1 battle garegga physics
idk any non shmup videogame where physics are in pi=4 type of distances
isnt pi for a square 8 ? seeing as the shortest radius of 1 will go around the circumference 8 times
@@ibrahim-sj2cr So if pi is the ratio of the circumference to the diameter it would be 4.
33:04 I love how that backpack gag, as presented, holds no extraordinary nature at all but so many levels of "dad editing magic" deep it does feel gratifying somehow.
I love how you phrased it xd
In America, we pronounce it "Lemnookie" because it rhymes with cookie.
Edit: This is also done to avoid confusion with the American band "Limp Bizkit", a common mistake in the late 90's which ultimately led to a scheduling mishap that resulted in 1 unexpectedly interesting and educational concert and 1 very disappointed maths conference audience. Although some argue that pronouncing it "Lem-nookie" only increases the associative confusion...
You’re a genius!
Wasn't that a Lemnizkit song?
@@reversev9778 The trick is to not be a Rookie
@@coyoteseattle Correct, when baking a Lemnookie Cookie, unlike a rookie, you do it all for the nookie.
@@coyoteseattle although you won't like where they stick it... Which brings us full lemniscate back to biscuit.
What I learned today: Matt lives with an identical clone of himself and he's also in possession of some sort of trans-temporal device with which he communicates with his future self. What a man!
I use such a device myself, actually.
See, I (present-me) predict that future-me will at some point indeed be in the middle of a grocery store and will have forgotten what present-me wanted him to buy. Since this happens more often than I'd like, I came up with a device, where present-I writes down what future-me should buy and then I sent that list straight into the future-me's back pocket. Since I like fancy names I decided to call it "grocery list". Quite catchy, isn't it?
I suspect similar technology might be at work here, too. But since it must be far more advanced than mine, we should call it something latin. Oh yeah, how about "script", since the main technique is writing stuff down?
Ah, genius!
@@aknopf8173 🤣🤣🤣🤣
Hey, he's a mathematician. Probably hacks reality every day.
The "clone" is most likely Matt from another part on the timeline visiting present-Matt.
You telling me this temporal device is trans?
I love how Future Matt could flawlessly edit that whole multiverse-Matt stuff but made a simple editing error between 16:00 - 17:30 :D
But future Matt hasn't made the error yet...
@@benholroyd5221 I guess he will have made it by the time the video has been watched.
@@michihaba4435 all we know is that he's future Matt, and that he is capable of communicating with the past.
It could be that he was in the past communicating with the further past, or he could be in the future, not yet having recorded the segment he will send back in time.
It's possible future Matt is aware of this error through reading the comments in this video, but can't change the script or else these comments will never be made and the universe as we know it could unravel.
@@benholroyd5221 Fair point. But if Future Matt will be aware of this error through reading the comments, it also means someone has already made the error though. Otherwise, neither the video nor the comments would exist. Maybe there was another version of Matt editing that part?
@@michihaba4435 or maybe it's a non linear non subjective ball of wibbly wobbly timey wimey stuff.
The cirare, or perhaps the Parker Squircle? Hear me out: the Parker Square and the Parker Circle may have been examples of giving it a go, but the true average of them, the Parker Squircle, is an example of vastly improving on something.
I want a Dr. Seuss-style book of Matt trying to convince people to try his lemniscate biscuits, corny rhymes and all.
That’s going to be just one recipe. The rest are ways to bake a pie to figure out inexplicably convoluted approximations of Pi.
And then the police come and confiscate his lemmiscate biscuits.
If he offered me a lemniscate biscuit, I wouln't risk it.
They need to be lemon lemniscate biscuits.
They should be stacked, but they probably wouldn't be stacked vertically - they'd be _leaning_ lemon lemniscate biscuits.
Amazing video, thank you for the mention!
I follow both of you!
Go Dan! I was so happy to hear the mention!
I think you two should collaborate. You could make a program that scrolls the names of patreon supporters.
Yeah, just discovered your channel becuase of him. Subbed.
the godfarther of mutimedia design undergraduates
I need more videos where the creator interacts with other versions of themselves, even past and future. I'm sure that took a HEFTY amount of scripting and even more tries to get the timing right between them like, it legit just sounds like a normal conversation between the three of them. You outdo yourself on EVERY video, I swear. I'm planning on making an official channel and you are definitely one of my muses
Honestly, way too many videos do this and it just drags things out longer than they need to be. I'm all for videos being entertaining but, like this video for instance could've been done in probably five minutes without the multiple sponsorships, built-in ads (how many ads were in this video is beyond me) and the talking to each other and the patreon credit sequence (we're turning into a Christopher Nolan film by this point). A myriad of physics, math, and graphic design videos have content creators talking to their doubles. It's a trope by now.
@@EmpyreanLightASMR youre exaggerating it way too much. "way too many ads"? theres one. also the actual ad + post credit patreon sequence is at the end of the video, after all the actual maths, so it doesnt really matter much at all
@@EmpyreanLightASMR it's not easy to just edit a conversation with yourself into existence, you really need to get the timings right and wait long enough for your future self to respond in time, it gets harder and harder the longer the segments are! It's also not easy to make an interaction between the 2 recordings too. how about you just enjoy stuff?
@@LindenF Not here to be entertained. Here to learn concepts, and quickly, because I only have so much time in the day and time between classes and exams. Glad you and everyone else have the luxury of time!
@@EmpyreanLightASMR If you want to you can get the sponsorblock chrome addon, you can disable Filler Tangent/Jokes and Endcards/Credits with it, but the segments are made by people with the extension so it may not be on every video.
In America, most people take a course called “Precalculus” in which one part focuses on graphing in the polar coordinate system. They introduce a handful of curves, including the the lemniscate, along with cardioids or rose petal curves to graph. Its not so much a ‘grand finale’ as in my experience they just give the equation and what it looks like, then ask you to try and graph it in different scaled versions or orientations, and thats it. We don’t really learn any properties besides how to graph them in polar.
I don’t remember anything about polar coordinates from precalc. RIP
In higher level calculus courses (calc 3) we used polar coordinates to make solving areas within of all the shapes mentioned above + combinations of said shapes much easier.
Most people? Wow, I never knew you were so well educated in Mathematics!
@@jg-reis Nah not most. The precalc class in my highschool and college didn't go much if at all on polar coordinates. not even graphing.
We did polar in my pre calc class but I don't remember doing lemniscates, mostly just cardiods.
That icing F looks like Matt invented a new constant symbol
Wau!
The constantly screwing up my lembiscuits constant.
Parker F
The constant 7. Which, to be fair, is pretty constant
Looks like Gumby
Matt : "- Let me know if you spot any other mistakes.
"
Well, Future Matt at 23:00 decides to skip the 1st decimal digit of the arithmetic mean (it should be 1), and it ends up saying that 1.1981 is super close to 1.981 never noticing the mistake.
I guess it's time for Future² Matt to enter in action.
I was looking for this comment. Haha thanks!
This!
Unwatchable
Yep, I was about to make a comment about it, but of course, someone else has spotted it first.
He also says geometric mean twice at 20:20
But also the clips starting at 16:12 and 16:44 are obvisusly the same clip shot twice...!
"The gamma function is not friendly." There's an understatement.
I also like his comment on perimeters. Look at fractals and their boundaries. You can have infinite perimeter length with finite area.
I was just about to say how good Matt was at writing with icing sugar and then he made a Parker F.
Me: existing
Matt: so have you ever wondered what the area of a Squircle is?"
*And that's the moment I started wondering what the area of a Squircle was*
I now have interest in what a lemniscate is.
I've also learned that my phone keyboard dictionary knows "lemniscate"
@@SgtKOnyx
Isn't it what you get when you sprinkle citrus juice on a flat fish? Yum!
@@trueriver1950 that pun there really threw me for a loop or two, I'd call it a lemniscate pun
Me: Obviously, he's gonna use polar coordinates and averages the distances to the center
Matt: Let's take the average between 2 and infinite as the exponents
Going by the title I had expected the obvious average to be the squircle with an area in between the square and the circle, or 3.5707 r^2… For n=4, the area is about 3.708, so too large, and for n=2.5 it’s 3.38, so too small. n=pi actually comes pretty close with 3.566! Coincidence?!?
When I saw the 4 in the thumbnail, I immediately thought about harmonic mean of 2 and infinity
Me too, the reciprocal of the average of the reciprocals, but I had forgotten its name.
@@TheMalT75 glad it wasn't just me this occurred to.
Could you find the average area of a square and a circle, then find the squircle with the same area, then find the n value of that squircle. (The average squircle)
The quality of this video is actually insane. Like, it’s sooooo good. The math is super cool (and explained very well), the skits are funny, and the production quality is through the roof. Hats off to you, this is now one of my favorite videos of all time.
"And if we actually crunch the numbers, which we can do..." Totally a missed opportunity to whip out a couple of baked number biscuits and take a bite out of them lol
Matt: "There's a whole family of so-called superellipses..."
Me: so this shape is clearly a superellipse with degenerate foci!
Matt: *squircle*
BTW, the EDITING on this one!
The gamma function method which Matt gave works perfectly for all kinds of squircles x^n+y^n=1 but I don't know how to extend the lemniscate method to other values of n.
"clearly"
@@EngineerWhen I was ver confused when I read the title but seeing the thumbnail I immediately realise what he was talking about.
The funny thing is that squircle is literally the technical term. There is a book called squigonometry which analyzes squircle trig functions (squine and cosquine)
Your brown paper explanation has objectively surpassed Brady's - yours is in much better taste!
you could say it's .. the icing.. on the -cake- biscuit.
"Objectively"->"Objectivity"
Hmm
@Amelia Kamel🌹 What the bot is this bot doing on a math vid
@@drenz1523 It's a rather recent bot.
LEMNISCATE is an anagram of CENTESIMAL (relating to the division of hundredths). Strange to see two long mathematical words being anagrams. The only other couplet (anagram: octuple) I can think of is TRIANGLE-INTEGRAL.
What's the fewest number of maths words needed to cover the alphabet
(We're meta-Parkering now aren't we)
@@philipwhiuk Good question - I'll see if I can come up with a solution. We'd first need to agree what constitutes a valid word, and then how closely related to mathematics the word has to be. For the first part, as an avid scrabble player I'll use the CSW list, which is the official tournament word list for English speaking countries outside of North America. It encompasses the whole North American TWL list, plus somewhere in the region of 20% additional words. Will get back to you soon on this.
@@philipwhiuk HOMOLOGICALLY FACTORIZED JUXTAPOSITIONAL WAVELIKE EQUIPROBABILITY is 5 words, but I think it might be able to be done in 4. Plus, it's debatable whether WAVELIKE is really a mathematical term.
I never knew that triangle and integral were anagrams until now
@@nicolinzini520this is incredible
I don't think people talk enough about how good your video descriptions are, you even link the videos you mention only once throughout the 34 minutes, I appreciate this a lot
Matt: "So squircles are a midpoint between squares and circles, but at what arbitrary point will we settle?"
Me: "I'd say at the point where the area equals the average of the two, that would be nice..."
Matt: "Oh no, that would not."
That would be interesting too, actually. What value of n would give you an area of 2 + pi/2?
I thought about this but without a easily solvable equation for squircle area, how would I calculate it
@@cQunc To solve that you would have to do something like this mess, but also adding differential equations
That would be cool but also a nightmare to calculate.
And you know, when you use the harmonic mean, like Matt did, I think we can call that specific squircle, the "Parker Squircle"...
Those Matt 2 and Future Matt complaining about Matt "1" were hilarious
Getting Deja vu from the unboxing video.
“I really hate it when those two fight.”
But it should have been Matt zero, or Matt sub naught.
This was a tour-de-force. The effort required must have been enormous, but soooo worth it!
Loved the lemniscate biscuit skit, Matt!
Oh, and as a curiosity, another way to define the unit square in the xy plane is given by the equation |x + y| + |x - y| = 2. Pretty cool equation if you ask me, but it wouldn't be practical for defining a squircle, I think.
Actually, |x+y|^2+|x-y|^2=2 defines a circle, which makes sense when you think about it - it has to be a conic section, for starters. Not sure whether the shapes you get for exponents between 1 and 2 are the same as some of the inner squircles here; I suspect so, but don’t know how to prove it, and you get *radically* different behavior for extreme values.
@@Pablo360able-- It is not appropriate that you used the word "actually," because you changed the subject by introducing exponents of 2.
@@robertveith6383 Actually, it's appropriate because I'm correcting the statement that the equation without exponents would be impractical for defining a squircle. The point is that, therefore, an intermediary exponent will do just that.
25:23 is the best special effect in the history of moving pictures.
Here......
you go!
If you told me a hollywood team didn't make this I wouldn't believe you
I legit burst out laughing at that part, like it's not bad, but it's shitty enough to be hilarous
Is there a ranked list of special effects in the history of moving pictures by quality? Could you maybe present it in a table?
@@gurrrn1102 if it can be presented as a spreadsheet that would be ideal
The AGM of 1 and 1/sqrt(2) (instead of sqrt(2)) is used in a very fast π calculation algorithm, called the Gauss-Legendre algorithm. The number of correct digits of π roughly doubles in each iteration.
Wait, pi is the AGM of 1 and 1/sqrt(2)? EDIT: Looked it up on Wikipedia. There's more bits to the formula. Still cool, though
wtf damn
I think the AGM algorithm would be a great pi day calculation
@@marcusorban2439 way too accurate for pi day
Would that allow a raspberry Pi to easily calculate 1e15 (2^50) digits in a few hours?
I come back to this every once in a while. Having made several personal comedy videos with free budget editing software I found off of the internet, this is one of my favourite videos on CZcams ever. Great humour, great editing honestly, very creative, and it’s an interesting topic. But it was just really amusing to watch you get creative with the edits and fourth wall breaks.
Fun fact! There's a special type of woodworking jig that can drill "square" holes, and it actually drills squircle-shaped holes!
Demand money back for false advertising....😆
Are you sure it's squircle and not a square with quarter-circle corners?
@@aleisterlavey9716 Tbh it gets close enough that a quick nibble with a chisel squares the hole right up. :)
But then most woodworkers don't even bother wasting their money on the jig and just drill a normal hole and do more nibbling with a chisel to make it square, so... LMFAO.
It's just an expensive reinvention of the wheel. Could probably see justifying its expense if one routinely drilled square holes so much that the tiny extra bit taken out in the drilling step saves time on the chiseling step.
@@vsm1456 Pretty dang sure! It's a weird mechanism that uses a single cutting bit to drill a squircle-shaped "square" hole that takes only a minimal amount of nibbling with a chisel to square it up properly.
Holes drilled by those bits are squares with rounded corners, not squircles.
When he said “do you want this back” near the very end I perked up like holy crap how’s he gonna do this, aaaand really enjoyed the self-aware humor in the response XD
If you time it properly it wouldn't be hard. Or he could pause the receiving side till it lines up, most people won't notice something like that.
He could have done it if the scrolling Patreon supporters hadn't stopped covering the seam. Matt 2 just put down the tray and then picked it up again from offscreen.
FINALLY! You have stopped drawing on food with permanent markers and started using edible lines instead! Such an improvement! I give you a thumbs up!
This is an escape hatch in case he ever needs to eat his words
I was really inspired to find the formula for the area of a squircle / superellipse with a=b given any radius from this video but I got stuck after a lot of attempts and decided to set it aside for about 6 months. Returning recently, I finally figured out how to do it with some methods I've seen in other trig and Beta function related integrals I've worked with over that time to get A = (4r² Γ²(1+1/n))/Γ(1+2/n).
I love your hand writing.
It looks so neat, when you explained at minute 24 or so.
Its so nice
Now we not only have a Parker Square, we also have a Parker Circle. ^^
Squcirle
A Pircle
A pickle
Parcle?
Parquarle‽
Fun fact: Certain problems related to elliptic curves are so computationally intensive to solve that we use them in public key cryptography schemes like ECDSA.
I would say that the computationally intensive part is the discrete log problem. The elliptic curve's involvement is just to define a handy finite field, and the math to do the field primitives is perfectly ordinary (and fast).
But the elliptic curves aren't ellipses and aren't really related to the elliptic integrals under discussion either
They really should be called "cubic curves" instead of "elliptic curves." Who thought it was a good idea to call a function with x^3 "elliptic?"
28:30 I'm glad you explained that was a pencil sharpener because, interesting fact, it looks like a coffee maker 😂
Oh Matt, I tried to define the Sqwuircle and its area and perimeter about 20 years ago, but you made it so much more fun an interesting. Love your work!
If you start to think of the different Matts as clones of a "Matt Prime", then it turns out Matt *Two* is actually the original that the others should be rebelling against...
...because One is not Prime.
Matt would argue that two and three don't really count as real primes, either.
That would make Matt 2 and 3 Parker-Parkers.
But in some senses it is the ultimate prime.
Or the primary prime.
Or you might say, Optimus Prime.
that's why they carefully referred to Matt 1 as "Main Matt" instead of "Matt Prime"
@@trejkaz also, primes that differ by 8 are called octimus primes.
Ah yes, my favorite writing instrument for mathematics. Frosting piping bag.
Eating in the back of class?
I can only wish I had a math teacher like you when I was a child, I might have learned some math. Though I can't follow all or even very much, honestly very little, it still fascinates to hear someone knowledgeable talking about their subject of expertise. Very entertaining presentation, and I also feel like I am learning something!
11:14 ... expecting a pun anytime soon about Matt 2 "8" the biscuit.
Last video: Matt finds out which word creates the pointiest vector, when typed on a keyboard
This video: Matt explains a mathematical constant with colored cookie frostings and infinity-shaped cookies
Matt's living the dream, as far as I'm concerned
An acid-fuelled dream ;)
Sometimes I forget matt is an actual comedian, it just makes all the unexpected, really subtle jokes way funnier, that stare in the credits and the kiwi-co section had me cackling
I felt that pun at 11:38 seconds before he "said the line". I don't know if others did too, but I suspict it.
Really excellent video, both in terms of content and production. I love your channel, Matt.
Now find the volume of a sphube.
Now I can finally calculate the area of the apps in my home screen.
great video, love the production and the effort to make something really special out of this video!!!
Thank you for the amount of work you put in your videos. Wow, just wow.
That ending is probably the best moment in Standup Maths history.
25:21 Matt's VFX are always so good that it's hilarious when he does stuff like this ahah
I was trying to look up a particular figure 8 shaped cookie from my childhood, and what I found instead is a Swedish/Norwegian cookie called a Kringla.
What’s *baked* into my memory is sugar cookies where we squeezed the dough from a piping bag with a star shaped tip, both figure 8s and just a short, straight line. And then we dipped half of the cookie in chocolate.
A small observation I found interesting, the harmonic mean between n=1 (which leads to the square on it's side) and "n=infinity" if we assume we can use infinity as a number (which leads to a square) is 2 which gives a circle. So in certain way a circle is the midpoint between a square and a square, which intuitively makes a lot of sense to me.
I demand 2021 calculators review video. Now i dont know what kind of calculators to buy my for family and friends for christmas.
I loved those reviews so much
I mean “popular” music references are fine and all, but why hasn’t anyone realised that the final scene was likely an Annual General Meeting of Matts? Where they used the Arithmetic Geometric Mean of Matt-1 and Matt-2 to determine Future-Matt’s n-value? (~1.45679… if you’re wondering)
For practical applications I use the diagonal. You make a function where you give the diagonal and it gives you back the exponent. Then you enter the ari.mean between the radius and half the square's diagonal.
Recently I made a crt shader in hlsl and to do the rounded corners I needed the squircle! it was such perfect fit too. Man, squircles are great.
IMO, "lemniscate" should rhyme with "figure eight," especially since I'm an OG Schoolhouse Rock fan.
hol up
Didn't school house rock start in the 70s
@@Slateproc Yes it did. And I was there. I even bought the LP.
Let me skate the figure eight (or lemniscate)!
I'd prefer lemni-skate, too . . . but the average viewer could get _skate-bored_ before the episode is over ;)
There's something fishy about that lemni-SKATE.
"now its time for the opening title"
SIX MINUTES AND 15 SECONDS INTO THE VIDEO, thats the content I live for
I appreciate the work you put into your videos!
That moment at the end where the patreon credits disappear and there's no seam between the Matts. Well played sir :D
Alternative idea for an average: Taking the inverse tangent of both numbers, take the average of their angles (a sort of average slope) and then take the tangent of this inverse average. You get the cube of the Golden Ratio as the average of 2 and ∞.
That's very nice indeed. Call it the Bisector Mean cuz its exactly the formula for the slope of an angle bisector.
I like the way you think
After some working out, given two numbers a and b, this "mean" can be written algebraically as k + sqrt(k^2 + 1) where k = (ab - 1)/(a + b) . For a = 2 and b --> ∞, k --> a = 2 itself and thus you obtain 2 + sqrt(5) , which is the cube of the golden ratio since φ^3 = 2φ + 1 = 2 + sqrt(5) .
"Playing board games with Tom Scott or something" hahaha, great end to a great video in all ways.
Pretty sure it's a hint at what Matt will be doing in his video on Tom's new channel Tom Scott Plus which has just launched.
@@MrDannyDetail that would make sense!
11:50 he didn't wanna risk it, so he missed it.
The interactions between the Matts are so cool, especially Future Matt! Totally didn't expect that
I forgot, and then realized halfway through, that Matt was drawing all the equations in icing. Nice touch.
5:30 The way you write infinity still freaks me out, and Numberphile's "problems with zero" was 9 years ago now xD
He writes it as the voicemail symbol
I agree, and I also find the way he writes x equally as freaky (it's just a horizontally inverted c back-to-back with a normal c)
@@janikarkkainen3904 that was how I was always taught to write it at school so as to not mix it up with multiplication symbols.
@@SimonHollingshead I've been taught multiplication symbol is either · or *, not ×, thus writing x normally is not an issue. To me it just looks sooo weird. The decimal point in the vertical center also freaks me out a lot.
@@janikarkkainen3904 that’s how you write x when it’s a variable, it’s done to disambiguate between it and ×, the multiplication sign. If you’re from a country that uses a different multiplication symbol you were probably never taught that technique. In Australia, though, this is the standard.
Another interesting thing about the squircle is that, as an implication of by Fermat's last theorem, at least one coordinate of all points along its perimeter must be irrational, except at the 4 points where it intercepts an axis.
This video is so good. Had my brain hurting with all the arithmetic, but the fun editing kept me in
Matt making smalltalk with himself at the end is hilarious
So what you're saying is that π = 4. Got it.
but only for a square-shaped circle
For a square. But in discworld, it equals 3 for certain shapes.
its analogous to 4 in squares
The sheer joy Matt emanates during the lemniscate biscuit bit is immense
this is genuinely one of the best videos I've ever watched. very fun!
Arguably, there isn't a nice way to write the area or circumference of a circle either, without inventing a hard to calculate circle constant (π (or τ...)).
Yes, but you only have to do it once. And pi appears in many other places (like trigonometric functions, spheres, elipses, and in physics)
@@pedronunes3063 You also only have to do the Lemniscate constant ϖ once, and it also appears in many places (like quartic trigonometric functions, spheres, spherical ellipses, and in many areas of physics). It parallels π in many, many ways, and many (most?) identities involving π have some analog involving ϖ. If π is the constant for doing analysis on a circle (line segment with opposite ends identified), then ϖ is the constant for analysis on a torus (square with opposite sides identified).
@@jacobolus i didn't know that, that's interesting
I will never understand how he can sync up a conversation with himself without any noticeable edits
I'm assuming he records one, then plays that back when recording the second
@@ad220295 And then plays that one back when recording the first, yeah. Pretty easy.
He freezes time during his stare at 31:45
And the future Matt takes a bite of his lemniscate biscuit and suddenly jumps to a special thanks cut at 33:34.
These were the only cuts I've noticed in the first time.
A lot of respect for Matt for doing this indeed, no easy stuff, probably spent more time than anticipated on getting this right.
Oh my god this is brilliant! For my first job I had to draw the 2d cross section of multiple copper wires squashed into cylinder (the wiring within an electric car engine motor). These shapes began as circles and were squashed slowly into squircles as you added more wires, or reduced the cross sectional area of the cylinder (I know technically they would be compressed to hexagons, but a squircle provided near-accurate predictions and was more simple).
I still remember my moment of pride, completing my first coding task ever, allowing a dynamically chosen number of wires to change the picture on the screen, slowly becoming more square as you added more.
Better yet, these wires had insulation and copper components, so drawing a compressed squircle within a squircle within a cylinder was quite the challenge! Ahh how I miss my old job.
For context regarding the Lemniscate in US education, at least for myself: it was briefly mentioned in Calculus 1(derivation with some low level, intuitive integration at the end) but the equation was broadened to be able to draw additional petals by changing the scalar on theta.
The important question is how many times we think we've been seeing Matt 1 when actually it was Matt 2... For example the sink spinning video, where we thought Matt took a sink on a plane to Australia, maybe it was just Matt 2. And who's to say that there's just 2? Maybe there's an infinite number of Matts and it's just Matt all the way down
Even in this video we probably only saw two Matts, since Future-Matt is likely - though not conclusively proven to be - the extension of Matt-1 or Matt-2 through 4D space-time, or even some sort of hybridisation of both their respective timelines.
That got me thinking… Do you suppose when Matt-1 and Matt-2 get together to determine Future-Matt’s n value (the value of n for Matt-n = Future-Matt) they held an Annual General Meeting of Matts and determined the best way of determining the correct n value for the relevant Future-Matt and used the Arithmetic Geometric Mean of the Matts in attendance?
@@wraithleader012 Future Matt has the same bag as Matt 2 (as proven by the biscuit lemniscate), so it would seem probable that this Future Matt as at the very least an extension of Matt 2, though it raises the question if Matt-n is from an n timeline, with their own bag, or if there are simply n Matts in the current timeline, with 1 shared bag
I just take the Parkarian geometric average Matt 1.6
StandupMatts?
@Amelia Kamel🌹 begone BOT!
Something I just like to imagine: the brown oven paper being brought by Brady.
Your content just gets better and better. The maths gets more and more interesting and the tropes become more and more entertaining.
loving your edits and commical self aware storylines. :)
looking forward to the Tom Scott Plus collab with Beard Matt :D
Tom Scott and Matt Parker are proven to be an amazing collab.
16:14 and 16:46 sound like different takes of roughly the same text.
was just about to type that
I liked the little peak behind the curtain... second take was better :D
I had to rewind to make sure I wasn't having a stroke.
@@Baiko I had rewind to check I wasn't having a stroke
To compute the "nightmare" complete elliptic integral of the first kind K(k), you precisely use the arithmetic geometric mean. Explicitly: K(k) = pi/(2AGM(1,sqrt(1-k^2)). So actually it is not really more complicated than what Matt presents afterwards.
..100℅ effort for this amazing, knowledgeable and interesting episode.
I already thought this channel was great, but this is just the icing on the Lemniscate!
Commenting before watching: I wonder if he's going to explore rectircles, triarncles, and pentarcles. Going up a dimension, you could explore the properties of a shpurbe.
Edit: he got to, and wisely insisted on ignoring, rectircles, aka super ellipses.
"Triangles"?
@@columbus8myhw Trircles.
"Shpurbe" is a terrifying abomination of a word. I will now use it daily with pride.
Sphube, surely.
@@columbus8myhw autocorrect did me in. I of course meant triarncles
Oh boy the ending scene got me laughing 🤣 top notch work Matt, really clever
You've out done yourself on this one, Matt! Well done :)
6:00 If you look at a vertical line as an "infinite" slope, sort of like how we call a flat line a zero slope, then we can accept 1 (a perfectly diagonal line) as the halfway point between 0 and infinity, 2 as the halfway point between 1 and infinity, 4 as the halfway point between 2 and infinity, etc. I think slopes are a pretty good analogy for the harmonic mean concept; also, the reimann sphere is cool: en.wikipedia.org/wiki/Riemann_sphere
Also the negative reciprocal of a line's slope ( -1/slope) is a normal to that line, so that kind of goes well with an "infinite" slope line normal to a zero slope line :)
@@wrOngplan3t that's true, most of the issues we have dealing with infinity come from the fact that we treat positive infinity and negative infinity as separate things. But the reimann sphere concept proposes that negative infinity wraps back around to positive infinity, which fixes a lot of the problems we have with taking limits, dividing by zero, etc.(for whatever reason this idea is controversial) Infinity doesn't necessarily have to have a sign, it can be sort of like 0 and for thousands of years, mathematicians didn't even know what to do with 0 so I think accepting infinity as a number is going to be the next step towards a better mathematical framework.
Hi Matt! The Earth is a squircle im a squircle Earther!
Squircle earth truther gang rise up!!!
🤣🤣🤣
Matt talking to past/present/future versions of himself brings back positive memories of send emails to "Future Me", and I love how happy it makes him.
When I lie down and watch videos on my phone, I often prop my phone up against a stuffed Squirtle. I happened to be doing this when I started Matt's video on the Squircle.
I love the different Mats interacting with each other it’s so funny and cool
Omg I loved the shoutout to Tom Scott: I bet Beard Matt is in-fact, actually playing board games with Tom Scott in an upcoming episode of Tom Scott plus Matt Parker.
Your sense of humour and montage are great