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Happy Pi Day! To celebrate I attempt to compute the digits of Pi using the “collisions” method, thanks to 3Blue1Brown for the idea! Code: thecodingtrain.com/challenges...
🕹️ p5.js Web Editor Sketch: editor.p5js.org/codingtrain/s...
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References:
📄 Playing Pool with Pi: www.maths.tcd.ie/~lebed/Galpe...
💥 Elastic Collisions: en.wikipedia.org/wiki/Elastic...
📓 Euler Method: en.wikipedia.org/wiki/Euler_m...
🥧 Additional Pi Day Code Examples: github.com/CodingTrain/Pi-Day...
Videos:
👁️‍🗨️ The Block Collision Puzzle: • The block collision pu...
🔢 Pi and Bouncing Balls: • Pi and Bouncing Balls ...
⭐️ Member-Exclusive Pi Day Prep: • Member Only - Pi Day Prep
🔴 Coding Train Live 172: • Coding Train Live 172:...
Related Coding Challenges:
🚂 #95 Approximating the Value of Pi: • Coding Challenge 95: A...
🚂 #140 Leibniz Formula for Pi: • Coding Challenge #140:...
🚂 #156 Peeking Inside Pi: • Coding Challenge #156:...
🚂 #161 Estimating π from Random Numbers with Euclid's Algorithm: • Coding Challenge 161: ...
🚂 #169 Pi in the Sky Game: • Coding Challenge 169: ...
Timestamps:
0:00 Introduction!
1:51 Basic code of the structure
7:00 Simulating elastic collision between two blocks
12:03 Simulating the wall
13:59 Adding the clack!
14:29 Counting the collisions!
18:09 Adding timesteps to control approximation
24:12 Adding constraints to speed up animation
26:47 Watching collisions upto 11 digits of pi!
28:46 Other methods to simulate elastic collisions and things to try!
30:50 Fake outro (and a special Pi Day song!)
Editing by Mathieu Blanchette
Animations by Jason Heglund
Music from Epidemic Sound
🚂 Website: thecodingtrain.com/
👾 Share Your Creation! thecodingtrain.com/guides/pas...
🚩 Suggest Topics: github.com/CodingTrain/Sugges...
💡 GitHub: github.com/CodingTrain
💬 Discord: thecodingtrain.com/discord
💖 Membership: ru-vid.comjoin
🛒 Store: standard.tv/codingtrain
🖋️ Twitter: / thecodingtrain
📸 Instagram: / the.coding.train
🎥 Coding Challenges: • Coding Challenges
🎥 Intro to Programming: • Start learning here!
🔗 p5.js: p5js.org
🔗 p5.js Web Editor: editor.p5js.org/
🔗 Processing: processing.org
📄 Code of Conduct: github.com/CodingTrain/Code-o...
This description was auto-generated. If you see a problem, please open an issue: github.com/CodingTrain/thecod...
#3blue1brown #elasticcollision #piday #eulermethod #p5js #javascript

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28 июн 2024

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Комментарии : 441

@guitoo1918 5 лет назад

This method is not time sensitive. Because of conservation of momentum and energy, Euler integration is not an issue. The problem is that when a collision happens, you let the 2 objects intersect with themselves and the wall. This leads to the small cube slowly drifting through the wall. If you just snap back the cubes positions after a collision, you should be fine. Technically the pieces don't even need to move, you just have to count the collisions respecting the alternating order of wall and cube collisions.

@Peds013 5 лет назад

I came to see if this comment was here, not too write it myself, but because I didn't think it was a problem but wanted to get confirmation :-)

@thetastefultoastie6077 5 лет назад

The problem here is that we don't know if the blocks collided until it's too late and they're already overlapping. So we must reduce the time step to be notified earlier of a collision occurring. You're suggestion of overwriting the position of the blocks breaks a few laws of physics and will introduce an additional source of error without actually fixing the original issue. There are two solutions: 1. Upon detecting overlap, compute how far back to reverse the simulation until the blocks are just touching. Do so, and then compute the collision and continue. 2. Before moving the blocks, measure the distance to the next collision. If this is less than the sum of the velocities then advance the simulation by a fractional time step such that they just meet. Then compute the collision and continue. In physics engines, method 1 is called a discrete simulation, advancing by a fixed time step and solving intersections retro-actively, very common in video games as it's relatively cheap to compute. Method 2 is called continuous collision resolution and is more computationally expensive and so sees less use in video games (Fun fact: this method was used in Diablo 3's bespoke physics engine to give us that sweet ragdoll physics)

@guitoo1918 5 лет назад

@@thetastefultoastie6077 The only thing that matters to get an accurate result is the order of wall and cube collision. And it's only decided by the sign of the relative speed of the small cube. As long as you maintain that order, anything goes. Position doesn't matter much as long as you ensure the correct order.

@TheCodingTrain 5 лет назад

Ah, thank you for this discussion. Indeed I did not explain this properly, oy! @Tasteful, if you would like to write a new comment (essentially what you wrote above) that is stand-alone I can pin it. I will address this during my live stream and maybe try to make a new version?

@Peds013 5 лет назад

@@thetastefultoastie6077 I understand what you're saying, but this isn't a time dependant problem, and can be solved analytically. Therefore the only reason for the time stepping should be visualisation, not too get the answer. The visualisation could be solved simply with the fix above but it means it'd run faster without grinding to a halt.

@justinhoffmann216 5 лет назад

I love that the video length is Pi (31:41)! Happy #PiDay!

@MaxPicAxe 5 лет назад

Was this intended?

@augustemmery-funch620 5 лет назад

@@MaxPicAxe yes

@DigitalMonsters 5 лет назад

Holy crap I didn't notice this, I love when youtubers take the time to add little easter eggs xD

@anthonytonev1357 5 лет назад

We have a mission - lets make the likes 3 141

@anthonytonev1357 5 лет назад

@Shreerang Vaidya let the sharing begin #Piday #Collisions #JavaScriptbenchmark

@sidalisaadi1961 5 лет назад

Calculates Pi On Pi day ... with a Pi long video ... how committed someone can be?

@tregi 5 лет назад

dont forget eating pie and singing the pi song

@anandsuralkar2947 5 лет назад

Lol

@anandsuralkar2947 5 лет назад

@@tregi yup

@charadremur333 4 года назад

Pi commited

@mohammadazad8350 4 года назад

approximately pi long

@gordonchan4801 5 лет назад

15:30 FUNDAMENTAL THEOREM OF ENGINEERING

@justanotherhotguy 4 года назад

Gordon Chan You had 3.14 likes but now you have 3.15

@Lord2225 4 года назад

e=pi=3

@Lord2225 4 года назад

and sin x = x ofc

@JoseGonzalezUwU 4 года назад

g/3 = pi = e = 3

@NStripleseven 3 года назад

Jose Gonzalez ah yes, g/3

@alliseth15 5 лет назад

the video length is 31:41 this is just excessive

@all69stoff 3 часа назад

And also: Unexpected and a Coincidence (maybe)

@rageace3942 5 лет назад

engineers: "that's kinda like pi, 3!"

@charadremur333 4 года назад

A few feet is no issue!

@Brahvim 2 года назад

`3!` Hmm, "Three factorial"? (That's `27`!) r/unexpectedfactorial? :wheeze:

@memerboi69.0 Год назад

timestamp: 15:30

@brando3465 Год назад

@@Brahvim I’ve never looked at a comment and wanted to make a comment about how awful it was until now. I don’t care that it was over a year ago, that was one of the worst things that I have read in my entire life. Please, never let any words escape from your head again, whether verbal, digital, or pen and paper. Your thoughts do not deserve to be heard.

@Brahvim Год назад

@@brando3465 _Thanks._ I've always talked to people about my RU-vid comments sounding cringe anyway. _Well this one was just stupid,_ and I'll have to make sure I make less of these. RU-vid is _just not_ the place for me to do these things, maybe. ...thanks.

@sangeetamankani5612 5 лет назад

Man For this you deserve 3,141,592,653,589,793,238,462,643,383,279,502,884,197,169,399,375,105,820,974,944,592,307,816,406,286,208,998,628,034,825,342,117,067 subscribers. And No I didn't copy-paste or see and type it. I remember 100 digits of PI using ASAP Science's song '100 digits of PI '!!

@zelioz848 4 года назад

Oh god.

@mebamme 5 лет назад

27:14 It goes like this, the wall, the block, the drawing loop, the ticking clock, the baffled Dan programming Pi collisions 🎶

@dingalong14 5 лет назад

You should be proud of yourself

@YesIKnowSillyName 5 лет назад

That's amazing

@harryfox4389 5 лет назад

p5 js p5 js

@msclrhd 5 лет назад

The baffled Dan composing Pillelujah! Pillelujah, Pillelujah, Pillelujah, Pillelujah.

@KnakuanaRka 4 года назад

What is that to the tune of?

@mebamme 5 лет назад

It's amazing how accurate you got it! Even having seen the 3blue1brown video, I was blown away by how the digits of Pi appeared, and the correct ones to boot! And all with so little code.

@Carlosdreaming 5 лет назад

What an amazing video as always! The video edition is every time getting better too. Great work!!! Thanks!!!

@nitinrangarajan7809 5 лет назад

This is frickin amazing :D Math and Computer Science are just so amazing! Happy Pi Day everyone

@funkahontas 5 лет назад

Agree !!! Pi is such a magical number , so mind bending where and how people come up with different ways to find it ! It's everywhere too !! Happy Pi day ! :D

@sirnicoosokhan4056 5 лет назад

You could also use this way: console. log(Math.PI);

@andrewzhang8512 4 года назад

Mahdi Nicoo that wouldnt be fun

@RubyPiec 4 года назад

@@andrewzhang8512 r/wozzles

@Slinx92OLD 4 года назад

@@andrewzhang8512 r/woooosh

@yentlvandamme 5 лет назад

All your videos are awesome! But this one must be one of the coolest and funniest I've ever seen!

@ItsDrike 5 лет назад

26:52 I love the song, you should upload a video just with the song

@bapolino733 5 лет назад

In the last few videos, your editing was so nice. If possible, please keep it up like this!

@sanderbos4243 5 лет назад

Props to the editor on this one. This is my favorite episode!

@WildAnimalChannel 5 лет назад

Knowing the velocity of both blocks, you could calculate the point in space and time where they collide. So you don't need time steps at all! (Except for animation purposes). If the time until collision is above say 1/60th of a second you could use a time step for animating. In fact that would give you a nice iterative formula for pi. (That would converge quite slowly!)

@colinjava8447 5 лет назад

Yeah I didn't use time or distance at all in my program to count collisions. It might seem like the small block could get crushed between the wall and big block if the big block is really big but I think what happens is there is trillions of small collisions that occur slowing the big block down enough so the crushing can't happen. At least in a mathematical model.

@markuzj.k9445 5 лет назад

Best PI day ever. Thank you so much dan!!! It would be cool to see if you graph velocities like in the 3b1b video

@technodruid 5 лет назад

Man, it's really cool you just see the physics through the math, like with hypothesising what the m=1 scenerio is. You're quite the polymath!

@nikensss 5 лет назад

I watched the videos from 3blue1brown when they were released and I also absolutely fell in love with the clacking, hahaha! I like seeing I'm not the only weirdo in this world :3

@Xnoob545 4 года назад

12:27 We can think of the wall as 256 high bedrock

@TheNutSlush 5 лет назад

This is my favorite video you've done!

@Blananas2 5 лет назад

Thanks for blowing my mind with this fact all over again. :)

@RogieWoah 5 лет назад

I loved that video, glad you could remake it!

@carlwheeser140 5 лет назад

Oddly enough, I actually did this a couple months ago! I coded the collision thingy! Neat

@followthetrawler 5 лет назад

That clack sound is the same as the clack that Clackers made, a toy from the late 60's that used to break kids wrists :) Good article on Wikipedia about them. Super video!

@mosk11tto 5 лет назад

Oh the concept is from 60s, I used to have one of those like almost 10 years ago

@nikkiofthevalley 2 года назад

That want dark, very quickly.

@XKCDism 5 лет назад

I am liking the new editing style

@8mrLuka8 5 лет назад

This is one of the best channel on RU-vid!

@OonHan 5 лет назад

AMAZING DEMONSTRATION!

@loic.bertrand 5 лет назад

The editing on this video is amazing !

@haval00 3 года назад

I loved that getting pi , and pi song and eating pi , thank you so much ❤❤❤

@jgcodes2020 5 лет назад

+3Blue1Brown needs to see this. Extremely laggy and inefficient, but extremely elegant.

@axeleblaze6691 5 лет назад

Amazing video as Usual!!! Always learn a lot from your Channel !!

@danielstefanescu4555 5 лет назад

Very cool Daniel. Interesting the creativity that you have.

@avi12 5 лет назад

29:47 The difference between float/double and BigDecimal, as well as the difference between int/long and BigInteger, is that using primitive types, the JVM is allocating a chunk of memory just for that primitive type's previously-set boundary, while as a for BigInteger/BigDecimal, the JVM is directly using the memory to store the bytes, which naturally results in a bigger usage of memory for the application. If you have a lot of RAM and you need high-precision for numbers, you can safely use BigInteger/BigDecimal. Just be careful not running into Infinite loops!

@fergusmgraham 5 лет назад

Good stuff Mr Shiffman!

@ShaolinMonkster 4 года назад

One of the most respected youtube channels. You are amazing.

@JordanMSeverns Год назад

this is the coolest thing ive ever seen in my life

@portalsrule1239 5 лет назад

I was just about to do the same thing! Good work! Happy PI day!

@adrieloliveira1463 3 года назад

This is awesome!

@anantmishra9813 5 лет назад

The best crossover, EVER!

@ahmedsonbaty6818 5 лет назад

Awesome Video man !

@ahmedelselly2553 5 лет назад

man i was feeling depression because i field to learn advanced javascript and u made me more interested in it u made me change my mind

@dawnstudios7813 3 года назад

A podcast with Grant and Dan in it has the potential to break the Internet.

@phemartin 5 лет назад

god i love this guy! awesome job!

@bridgest99 5 лет назад

This may be my favorite Pi video ever!

@justkeerat 5 лет назад

I did this in processing myself and after 7 digits it was just too slow.. I can't believe it went till 9 digits at such a good speed. But it's super impressive. I love how we all enjoy coding mathematical ideas that just make programming fun😂❤️

@AngelGonzalezM 3 года назад

You make me feel happy. Thanks

@lion2808 5 лет назад

Nice hint with the video length (31:41) And offcours awesome video as always I find it cool how you are so motivated and you actually made me want to learn a few digits of PI myself so I made an app that lets you train PI like a vocabulary trainer. I think you would like it

@musicdudejoe263 4 года назад

Thank you for the serenade in pi, much appreciated.

@MarsCorporations 5 лет назад

A Good way would be to calculate the "exact" collision point. Then you could calculate the amount of time that the small block needs to hit the wall, add v*time to both, calc exact collision point, repeat.

@user-sq9fw6kf1l 5 лет назад

Dude you are awsome!!! continue the good work

@Naej7 5 лет назад

I love the clacking too !

@justcallmesteve9123 5 лет назад

Thanks m8 i was thinking about that video for a while now.

@theaveragecoder6182 4 года назад

when I study too much , I just take a break and watch your videos . Great work , you are making this world a better place by making silly mistakes ;)

@itsnottylor4011 5 лет назад

That rendition of Hallelujah was beautiful.

@shaileshrana7165 4 года назад

This is your best video. I love it.

@RicoGalassi 5 лет назад

another awesome video!

@fNktn 5 лет назад

awsome as allways :) only thing missing is having the block scale based on their mass

@bobingstern4448 3 года назад

The song was the best thing ever, you should make an album!

@christianjt7018 4 года назад

That was an awesome project :)

@yurisugano6638 5 лет назад

so glad I am alive to see this

@tekoreypy 5 лет назад

Awesome name "collision clacking magic wonderfull thing!" , That's the coolest name ever!

@joaovictormendes2293 4 года назад

That was amazing

@pashevka 5 лет назад

This is wonderful

@techbytefrontier 4 года назад

Ok, so you were singing with the amazing grace melody. gotcha , divine number.

@kossboss 9 месяцев назад

The man can code and serenade!

@benjy6306 5 лет назад

:D I tried to make this simulation when it came out and it it worked but was rly buggy because there box went on the the other side of the "wall" thing Thank you so much :D

@samkimber6747 Год назад

You can also simulate/calculate pi in different bases by adjusting the mass ratio between the blocks! You get pi in base ten if the ratio is 10^2^n, you can do binary with 2^2^n, hex with 16^2^n, etc. You have to convert from base 10 to the target base, of course.

@santhosh6700 4 года назад

Belated pi day wishes dood,...I am new subscriber...thank u for made this video...I am gonna make this concept in unity(using c#)

@TheCodingTrain 4 года назад

Oh cool! please share when you do!

@syedmuhammadaliraza3069 2 года назад

the video was fab and the song was terrifying 🤣😂

@NonTwinBrothers 5 лет назад

Very nicely edited video

@BloodyScythe666 5 лет назад

phantastic how this works. would be interesting how this correlates to a circle

@luisisaurio 5 лет назад

Watch 3blue1brown’s video

@Bruno-ds8ze 5 лет назад

Amazing

@hankhill- 5 лет назад

I love you. Great video!!!

@skepticmoderate5790 5 лет назад

You could make the number of time steps dependent on the distance to the wall. That would speed up the longer calculations significantly.

@ForEverybody 5 лет назад

You are awesome all the time.

@AJMansfield1 5 лет назад

30:10 For the optics method, the trick is to use complex numbers to represent the angles, rather than explicitly dealing with angles or relying on any kind of trig function. Using the small angle approximation you can construct a complex number for a particular angle 𝜃 as just 1+𝜃i, and then n*𝜃 is (1+𝜃i)^n. Here's a quick python implementation: ideone.com/T4UCnV For the kinematics method, instead of a fixed timestep you can directly compute the time until the next collision as dt = (x1+w1-x2)/(v2-v1) and make that as one single step; then to animate it you can either interpolate between timesteps or you can have a separate fixed-timestep integration that you re-seed from the main integration at each collision. This also lets you play the clack sounds at a more granular time resolution rather than forcing it to be quantized to the animation framerate. If you're interested I have a python implementation of this that works for an arbitrary number of blocks in an arbitrary number of dimensions, including an interpolation mechanism. At this point I don't have anything for generating the actual animation, but I can at least plot graphs: gist.github.com/AJMansfield/00d69e1488c2b1eb56b8c4da2ca739dc Alternately, you can even forego tracking the block positions altogether, since we already know what order the collisions happen in and the position doesn't figure into the momentum transfer equation. If you take this route you can also simplify things even further and perform the momentum transfer as a single matrix multiply rather than as a number of separate steps. Here's another quick python implementation of this method: ideone.com/jPBh8C

@TheCodingTrain 5 лет назад

Wow, thanks for this thorough explanation and code samples! Much appreciated!

@grevel1376 5 лет назад

it was really exciting

@lapischicken 5 лет назад

Love it

@nileshshukla298 4 года назад

Your videos time also represent first 4 digit of pi😁😁😁.. love your video 🙌🙌🙌

@RAWRCoding 5 лет назад

Really interesting video :D

@NStripleseven 3 года назад

Your computer must be insane to be able to handle that whole thing in any reasonable amount of time.

@chriscalver8595 Год назад

great video

3 года назад

The most effective way to calculate Pi by far.

5 лет назад

I love it when you normalize the speed of the video just to make us listen your pi song hahdhahshhsjjsdjjdjd so nice

@harrietgoogledrive717 5 лет назад

Super challenge.

@dretheblack 2 года назад

i love this guy

@Domzies 5 лет назад

We have an anual competition at our college, where people recite the numbers of pie, last year a 12 year old girl recited over 900 decimal numbers

@slugginatubb 2 года назад

I love how I understand all the coding stuff he is doing but I suck at coding myself

@moiquiregardevideo 5 лет назад

I think that using the speed of both blocks after the last collision can bring more digits to pi ; possibly up to 8 digits for 64 bit double floating point. The slope of that line represent the best rational approximation to get a few more digits of pi. The current code compute 10 digits of pi and double are 18 digits total. One extra twist of optimization could be to avoid redrawing the cubes if they didn't move by a whole integer, which is one pixel. We expect no more than 1 order of magnitude improvement here. This code reminds me the bresingham algorithm to draw circles using integers only.

@peternguyen1899 5 лет назад

This guy belongs at NASA.

@archiegarg1958 4 года назад

This guy is more of a comedian than a programmer

@ziomanzo 5 лет назад

you must have a common ancestor with the nutty professor 😂

@alastairleith8612 Год назад

amazing Π fun. I'd like ou to show basic workings for how physics formulas are derived. it's not that hard to run through conservation of momentum and energy quickly. years since I did it but we only had calculators and spreadsheets to do such models in those days!