"Found a pretty optimized way to make a circle in Desmos. Maybe someone could try to shorten it a little bit." Music made by me. Link to graph: www.desmos.com... Happy Pi Day :)
@@blairhoughton79180! Means you are making a set containing every natural number before 0 and 0, which means the set only contains 0, so it reports having 1 combination
@@ok-tr1nw The definition of factorial is the product of all the positive integers up to the argument. Putting 0 in a product zeroes it. Factorial isn't really defined outside the positive integers. What's happening if 0 needs to be in the domain is that we should use the gamma function instead of the factorial. We get the same result for integers greater than zero, but then we get a value for 0. Calling it 0! is borderline math-illiterate, but keeps the computer from having to cast in and out of floating point to call gamma...
@@ok-tr1nw I think you're thinking of the binomial theorem for 0 choose 0, which has three factorials in it (n!/r!•(n-r)!), but doesn't really, because 0! doesn't exist because 0 isn't really in the domain of the factorial mathematically, so it really has three gammas in it. And gamma(0)/gamma(0)•gamma(0-0) = 1/1•1 = 1.
I'm sorry, *this formula is actually NOT draw a "unit" circle* , but one which radius is _10/11_ . i found that desmos made trouble in this part of formula (you can find in video around center of 1:01): _floor(distance((distance((0-0,0+0),(1,1))^2,distance((2^2-1^1,3),(2^2+1^1,3))),(2floor(e),sqrt(ceil(π)))_ if we simplify this, we get: *_floor(4-sqrt(2)^2)_* We can absolutely sure that this equals _2_ , but asking desmos, it returns _1_ . ( the reason is that _sqrt(2)_ is irrational, computer can not express _sqrt(2)_ precisely due to infinite decimal. if you cannot believe, you should try this in desmos: _sqrt(2)^2 - 2_ ) Since desmos draws a unit circle even though the results are wrong, unfortunately, that enormous formula doesn't draw a "unit" circle... Well yeah, the title is correct because it doesn't say "unit" and that formula actually draws a circle. Although, Great job! ps: If we simplify that gigantic formula according to desmos rules with a lot of effort, we can finally get this: _(sin(2πt), cos(2πt)) * 5/(6-1/X), where X = _*_floor(4-sqrt(2)^2)_*
i dont know if this is correct, i dont even care. I just love the idea that someone out there took the time to flex their knowledge to hit someone with the "um, ackchualley"
@@highviewbarbellwell they are the fundamentals in a way,also it shouldn't be hard to figure this out. A kid knowing the triangle square law can figure that out easily.
It is actually very cool. The link for the graph is in the description. It is nice to see some very random part of the equation just changing the radius of it haha
The mathematical equivalent of chaotic order. Something simple made complex, while retaining itself. It's a thing of beauty, glad to be the 907th viewer of this
Lol true. Although it's understandable: mathematicians want to get to general rules which work in most cases possible, while engineers just want the building to stay up lol But yeah it's funny how sometimes maths do such a big trip jist to prove 1+1=2 (it's like a 500 pages dimostrations i believe ahahaha)
yeah basically all that complex stuff goes to 1 or 0 and cancels itself out of the equation. the main part of the equation is still Sin (2pit), cos(2pit) but its using identities to make significantly less simplified and then adding on a bunch of randomness that either turns into *1 or +0. a few of the chunks of the equation are just making a really scary looking version of +1.
For those who want to understand, he stars with the simple equation of a circle and multiples it by 1 in form of big expressions. Those big expressions are a series of 1-1+1-1+1 that eventually cancels and gives a result of the simple circle equation times 1. Simple but a clever idea to try and impress any who may not understand
Squidward: What the?! A perfect circle?! Do it again. Show me your process. Jake Walker: Well, first I write this simple equation in Desmos. Then I add some square roots. Then I add some more derivatives, integrals, and summations. Then I add a bit of factorials, permutations, and combinations. Then I add a few more exponents, absolute values, floors, ceilings, matrices, trigonometric functions, and logarithms. And one, two, three - a circle…uhh thingy.
Reminds me of a programming module I replaced last week. It was roughly 100k LOC to change the LED color on a specific device, and I replaced it with 40 or 80 LOC, depending on how you count it. To me, this video roughly illustrates the complexity level of average software, compared to what's actually necessary.
You can make custom colors in Desmos using HSV and RGB functions. If you set a variable equal to one of them (like "A = rgb(134, 45, 256) for example) you can use the color in other expressions just like you would with the 6 colors already available. The buildings are made up of 4 rectangles, being the front, top, bottom, and side. Since only one side of the building is shown, I don't need to account for the other side (e.g. if its to the right of the camera the left side is shown, if its to the left the right side is shown. If the buildings are on the left side of the screen then I just flip them so the other side is shown.) The back side is also never visible, so I only use 4 polygons for each of them and only 4 colors per building. Colors can be stored in lists and whenever you use a color on an expression, the colors in the list will be applied to each of the parts graphed. (So if you had a color that was made of 5 listed values and then graphed 5 points, then the first point would be the first color, the second point would be the second color, and so on.) The colors were sort of just done by eyeballing what felt right. The front side is darkest, the sides and bottom are a little brighter, and then the top parts are the brightest. I made a second darker version (the lighting was multiplied by 0.8) to give a bit of variation. Since the rectangles are made in a specific order, the color always lines up with each of the sides and make it have the right lighting. Hopefully this makes sense and helps!
Fun facts: The actual parametrization is at the very top line with the trig functions, all the rest reduces to 1. This actually relies on a few Desmos bugs to run: notably one instance where distance((0,0),(1,1))^2 is calculated to be just a tiny bit above 2, thus later when a floor function is taken this effect is amplified to give the wrong (but desired) answer.
![🎤 จับฉลากร้องเพลง x P’ #XXSIVK [EP.1] (2/2) เพื่อนจับได้คำไหน..ต้องร้องคำนั้น เริ่ม! 💓🎶 #MXFRUIT](http://i.ytimg.com/vi/1bJvMJXmeS4/mqdefault.jpg)
![Megan Thee Stallion - Neva Play (feat. RM) [Official Video]](http://i.ytimg.com/vi/TpYTyAaTRts/mqdefault.jpg)
POV: your teacher said you should use the long method
a reply here
And on todays test I recomend using the long way and dont forget to show your work for extra marks:
POV And you still get the answer as wrong because "I said the long method, not the longer method"
The long method:
not just long but very very long. hmm😈😈
I love the wall of 1/1. It must be there for emotional unsupport.
As well as the sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(1
I'm pretty sure almost all of these equations are just fancy ways of writing either 1 or 0.
@@DingleberryGaming56 it’s load bearing roots.
@@BrianAwesomenes Perfectly balanced, like all things should be.
Same as starting with 0!
"I paid for the whole CPU, I will use the whole CPU"
I used the whole cpu by getting it's temps to 108C°
@@masonboone4307 my pc reached 150°C just by watching this video
@@lucaslautaromartinez7939
🔥😤🔥
0:20 biblically-accurate integral
Real
be not afraid
be not afraid
int(d)dd from 0 to 0.
½d^2 evaluate from 0 to 0
= 0
Bible = zero
@@FreshBeatlesfor that specific integral that is
Imagine seeing this on your math homework and all it asks you to do is simplify it
Simple. I take a white out pen-
You gave me an idea for my future students.
When smart kid just writes x^2+y^2=1 because they can tell that it's just a circle
@@simonwillover4175 without the graph of course.
Honestly this looks easy, albeit quite long.
That 0 factorial at the very beginning is honestly the cherry on top
0 factorial is nice but I'd go with ((0!)^0)^2 for extra flavour
I hate that 0!=1, but love how it simplifies loops...
@@blairhoughton79180! Means you are making a set containing every natural number before 0 and 0, which means the set only contains 0, so it reports having 1 combination
@@ok-tr1nw The definition of factorial is the product of all the positive integers up to the argument. Putting 0 in a product zeroes it. Factorial isn't really defined outside the positive integers. What's happening if 0 needs to be in the domain is that we should use the gamma function instead of the factorial. We get the same result for integers greater than zero, but then we get a value for 0. Calling it 0! is borderline math-illiterate, but keeps the computer from having to cast in and out of floating point to call gamma...
@@ok-tr1nw I think you're thinking of the binomial theorem for 0 choose 0, which has three factorials in it (n!/r!•(n-r)!), but doesn't really, because 0! doesn't exist because 0 isn't really in the domain of the factorial mathematically, so it really has three gammas in it. And gamma(0)/gamma(0)•gamma(0-0) = 1/1•1 = 1.
You'd be hard pressed to find a way to optimize that circle even more than you've already optimized it. Also, fantastic music my dude.
*unoptimize
Wait until he learns about trailing zeroes
He made this music ?! He strong in maths AND musics ? I think he need to have an big weakness or he is not from this word
@@redstocat5455bro can calculate his next note, live onstage.
@@redstocat5455 he didn't make the music, Shazam says it's Paradise / Chris Alot
Edit: it's not that one
man made his equation into a four-story building
that's quite the hotel
@@aadenboyIt even came with a buffet
Bro gave the equation a functioning economy
I think the building is a bit more circular, right?
NAh, that's not 4 story - it's a skyscraper
I'm sorry, *this formula is actually NOT draw a "unit" circle* , but one which radius is _10/11_ .
i found that desmos made trouble in this part of formula (you can find in video around center of 1:01):
_floor(distance((distance((0-0,0+0),(1,1))^2,distance((2^2-1^1,3),(2^2+1^1,3))),(2floor(e),sqrt(ceil(π)))_
if we simplify this, we get:
*_floor(4-sqrt(2)^2)_*
We can absolutely sure that this equals _2_ , but asking desmos, it returns _1_ .
( the reason is that _sqrt(2)_ is irrational, computer can not express _sqrt(2)_ precisely due to infinite decimal. if you cannot believe, you should try this in desmos: _sqrt(2)^2 - 2_ )
Since desmos draws a unit circle even though the results are wrong, unfortunately, that enormous formula doesn't draw a "unit" circle...
Well yeah, the title is correct because it doesn't say "unit" and that formula actually draws a circle.
Although, Great job!
ps:
If we simplify that gigantic formula according to desmos rules with a lot of effort, we can finally get this:
_(sin(2πt), cos(2πt)) * 5/(6-1/X), where X = _*_floor(4-sqrt(2)^2)_*
i dont know if this is correct, i dont even care. I just love the idea that someone out there took the time to flex their knowledge to hit someone with the "um, ackchualley"
@@AidanNaut0 Absolutely agreeable
He did a great work, no matter whether it is correct or not.
bless you, child. now, please touch grass
@@cvspvrhe is, quite literally, grass himself
get well soon
POV: Math is just a game to you and these are the levels.
can anyone help with the Long Division level? i have a major skill issue :(
@@Jundiyun Skill issue in long division? how tf, its the easiest thing ever
@@4fgaming925 i have the "Autism" debuff trait
@@Jundiyun I have adhd lol
@@Jundiyunreroll
Teacher: "You need to use the method i taught you"
The method taught by the teacher:
me: blinks for 0.1 second
the teacher's board:
Truly the circle of all time
This whole video feels like the last five minutes of an exam
"The test is only hard if you didn't study"
The problem that is worth half your grade (they barely mentioned the topic once):
@@webaazul2500FR 😢
@@webaazul2500I had to deal with such situation once for a formula that the professor has clearly said won’t appear in the exam 🤦♂️
desperate moment when you try to remember whatever equation that MAYBE relevant to the last question
@@fernando4959 "Random bullsh*t go!" moment
I miss the days when it was just
x²+ y²= r²
r=1
x²+y²=r
And back when there weren't any letters
@@phantomicco6068 what does it have to do with letters? how are you gonna represent a circle without letters?
Kids wish, they hope to do great things but also hope that everything will be as easy as 1+1=2@@lox7182
do NOT let this guy cook in math class 💀
meth class
Dude just invented math calligraphy: displaying simple thing in the most perplexing way.
fr
i saw this monstrosity in the desmos discord server, you are an absolute menace to society and i love you for it
Wait, desmos discord server.
Can you share the link to that server?
@@Mystical_Poet I think invites are paused for the server so unfortunately I can't
@@kono152 alright, no problem. It is what it is.
"Trust the process"
The process: ⬆️➡️↩️↖️⤵️↪️↙️🔄➡️↘️↔️
The result: ○
136 likes? no replies? lemme fix that
such an art
"la matematica e facile" la matematica:
@@lorenzodiambra5210 translation (without seeing): maths is easy, maths:
My mans turnd that equation into a Metroid map
That’s it. You’ve convinced me to do one for myself. And trust me, it’ll be the messiest piece of math I’ve ever done.
Progress update please
@@fireninja8250 Going well, up to a whole screen’s worth. But I’ll have to leave it there for now since I’ll be busy.
@@gallium-gonzollium make a vid
Commenting on here so that I can return back later to check on the update...🎉
Update: nearly ready! should be uploaded in an hour or so!
fun fact, the same equation can be written as x^2 + y^2 = r^2, in which r is an adjustable radius for said circle
He picked the long method
stop teaching shortcuts so early. These kids need to understand the fundamentals first.
@@highviewbarbellwell they are the fundamentals in a way,also it shouldn't be hard to figure this out.
A kid knowing the triangle square law can figure that out easily.
@@boltez6507 r/wooosh
@@boltez6507they were joking that this video's final result is "the fundamentals"
This method was so effective my internet stopped working, the video started buffering and I was greeted with a spinning circle.
Good job 👍
Would be fascinating to see what would happen to the graph if you change a single value.
It is actually very cool. The link for the graph is in the description. It is nice to see some very random part of the equation just changing the radius of it haha
Probably grenades the computer
I was simplifying it sometimes and if I screw up the whole circle just disappears half the time 😅
me: changes one number
my laptop: *AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA*
The mathematical equivalent of chaotic order. Something simple made complex, while retaining itself. It's a thing of beauty, glad to be the 907th viewer of this
This is the very definition of what my high school AP math teacher called "killing ants with sledgehammers!"
And sledgehammer failed to do it bc miss shot
Happy Pi Day!
Mathematicians unnecessarily overcomplicating things and making fun of engineers and physicists for trying to simplify and making the most out of it:
They don't... COM is maths but it was to solve complex problems
Lol true.
Although it's understandable: mathematicians want to get to general rules which work in most cases possible, while engineers just want the building to stay up lol
But yeah it's funny how sometimes maths do such a big trip jist to prove 1+1=2 (it's like a 500 pages dimostrations i believe ahahaha)
This guy has crazy software engineering potential... I mean.. He is doing graphics programming using just math 💀
The fact he used euler's identity for this is fascinating.
Your music is one of the most thematically appropriate musical scores of all time
You forgot the letters "ma" on the front of "thematically".
when your equation starts to look like a spaceship, you should get a new major
I'm more impressed by the fact the graphing calculator can handle all that.
Amazing. The 1/1's were really a great touch
When the teacher says "using shortcut will deduct points". So you use the most complicated method you know.
Imagine showing Newton this like "The way you know to make a circle isn't 100% accurate. Instead, this is how modern scientists do it:"
As a 7th grade student I can confirm that I am confused and do not understood any of this.
*understand
As a graduated high school student I can confirm that I am confused and do not understand any of this.
As a math major I can confirm that I am confused and do not understand any of this
As newton himself I can confirm that I am confused and do not understand any of this.
As the God of math, wth is this?
Choosing to integrate with respect to d is truly diabolical behavior
WHAT DOES THAT EVEN MEAN? I'm in Calc 3 and I just can't comprehend that
@@cosmicpanda7043By convention we don't use d as a variable because it is used to write the differentials (e.g. dx, dy)
@@xgr369 Oh so it was literally just denoting the variable d. I was wondering if it was some crazy concept I'd never heard of
the most astonishing to me in this video is, that desmos supports all these calculations
i'm literally obsessed with the music wtf it's so addicting to my ears
i love the pure chaos exhibited by the music. absolute banger video
Imagine if it didn't even end up as a "perfect" circle
it didn't
this is like a final boss you'd see in a math game
This guy has actually made an animation called Maths: Final Boss
On a Desmos Calculator
The electricity to render this circle can offset the entire global carbon footprint
lol
Powered by a B class stellar body and 7 whole grams of Adderall
Teacher: Show your work
The work:
I always wonder why some processes in Physics can have such simple equations when I would expect them to look more like this
You did the music too just to make this suffering funnier, and I thought I found dedicated people before
But those 10 square roots tho lmaoooo
POV: My irrational overthinking versus what the situation demands
the part that cracked me up the most is the repeated square-roots in the middle of the whole thing LMAO
Everyone else is talking about the equation, but I wanted to say I really enjoyed the music as well, it's cool that you made it yourself!
Can't wait to see BriTheMathGuy try to simplify this
Imagine you find this and with no pressure you simplify it grabbing time here and there for a week just to find out it's a simple circle.
Beautiful...
Does most of the equation just cancel out or does it actually add anything to the circle 😂?
yeah basically all that complex stuff goes to 1 or 0 and cancels itself out of the equation. the main part of the equation is still Sin (2pit), cos(2pit) but its using identities to make significantly less simplified and then adding on a bunch of randomness that either turns into *1 or +0. a few of the chunks of the equation are just making a really scary looking version of +1.
Impressive. Very nice. Now let's see Paul Allen's Desmos circle.
"Simplify this equation"
me: *dies*
For those who want to understand, he stars with the simple equation of a circle and multiples it by 1 in form of big expressions. Those big expressions are a series of 1-1+1-1+1 that eventually cancels and gives a result of the simple circle equation times 1.
Simple but a clever idea to try and impress any who may not understand
me when I tell the kids in undergrad intro quantum that the wavefunction is just a section over some complex line bundle
The hardest part of this is actually finding the variable t, and realizing that this whole thing is NOT a constant
this hurts
that is both terrifying and beautiful at the same time
Squidward: What the?! A perfect circle?! Do it again. Show me your process.
Jake Walker: Well, first I write this simple equation in Desmos. Then I add some square roots. Then I add some more derivatives, integrals, and summations. Then I add a bit of factorials, permutations, and combinations. Then I add a few more exponents, absolute values, floors, ceilings, matrices, trigonometric functions, and logarithms. And one, two, three - a circle…uhh thingy.
0:19 sounds so beautiful
That One Unemployed Friend On A Tuesday:
that is a beautiful looking equation i must say
Your music is better than Alan's 😅
Reminds me of my young self stacking as much formulas I've recently learned to make "the hardest" math equation
Biblically accurate circle
yes, king, get postmodern with it
genuinely some of my favorite desmos art.
You make a song as fire as this and you don't even release it? Craazyyyy
"Music made by me" bros blessed fr
Make a video on solving the equation step by step.
Reminds me of a programming module I replaced last week. It was roughly 100k LOC to change the LED color on a specific device, and I replaced it with 40 or 80 LOC, depending on how you count it. To me, this video roughly illustrates the complexity level of average software, compared to what's actually necessary.
Thank god I won't ever have to calculate that...
My future teachers laughing behind my back:
alternate world where rather than asking you to "simplify" math problems ask you to "complexify"
the music was made by you too?? wow you have a lot of talent
That √√√√√1 is glorious
Hey, i am your 1000 subscriber.
Congratulations!
expanding same thing and deviding and multiplying the same thing makes it cooler
I don't know what I just saw, I'm not interested in knowing too, good video
The empty brackets got me
Me too.
Nice. Now make the radius 2
The way the circle was already formed several times 😂
Average last question of the exam:
Bro is that kind of person who makes math a problem
Yo man! I have a question involving one of your previos arts in desmos, how did you make the color from the buildings in the city desmos art?
You can make custom colors in Desmos using HSV and RGB functions. If you set a variable equal to one of them (like "A = rgb(134, 45, 256) for example) you can use the color in other expressions just like you would with the 6 colors already available.
The buildings are made up of 4 rectangles, being the front, top, bottom, and side. Since only one side of the building is shown, I don't need to account for the other side (e.g. if its to the right of the camera the left side is shown, if its to the left the right side is shown. If the buildings are on the left side of the screen then I just flip them so the other side is shown.) The back side is also never visible, so I only use 4 polygons for each of them and only 4 colors per building.
Colors can be stored in lists and whenever you use a color on an expression, the colors in the list will be applied to each of the parts graphed. (So if you had a color that was made of 5 listed values and then graphed 5 points, then the first point would be the first color, the second point would be the second color, and so on.)
The colors were sort of just done by eyeballing what felt right. The front side is darkest, the sides and bottom are a little brighter, and then the top parts are the brightest. I made a second darker version (the lighting was multiplied by 0.8) to give a bit of variation. Since the rectangles are made in a specific order, the color always lines up with each of the sides and make it have the right lighting.
Hopefully this makes sense and helps!
"Wrong way" ❌️
"Long way" ✅️
Btw thats pure art lmao.
This video is why there's way more people than just gamers that need to touch grass...
Teacher Monday morning be like: a small simplifying problem.
This should be in animation vs. Math
Thanks! I'll keep this in mind when I want to draw a circle.
Fun facts:
The actual parametrization is at the very top line with the trig functions, all the rest reduces to 1.
This actually relies on a few Desmos bugs to run: notably one instance where distance((0,0),(1,1))^2 is calculated to be just a tiny bit above 2, thus later when a floor function is taken this effect is amplified to give the wrong (but desired) answer.
I like that this technically is a true mathematical expression, if you where to write this it is 100% valid
Proof that x=x be like
very innovative way to efficiently generate a circle! (Good music myman love it)
Искусство лить воду
equation so complex it probably has its own immune system
Link?
www.desmos.com/calculator/wpbwv5axzj
I just added it to the description as well
@@jakewalker6thanks!!!
When designing ultra high level magic spell just for purpose of drawing circle💪💪💪
teacher: why you don't use my method
the method:
I fully thought the thumbnail was the blueprint of a submarine