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Amazing explanation , thank you!

Wait weren't square roots heresy in ancient greece ?

This is the Husband Store joke lol.

I think there is no "print" in the full code, so when I run full code it doesn't work. how can I run this code?

FR: Je ne connaissais pas cette technique. :O EN: I didn't know this method. :O

It is interesting to notice that you obtain the same result in the same number of iterations with a slightly simple formula: Xn+1 = (Xn + value/Xn) / 2 Same result with less machine cycles

nice video, thank you for trying to do it historically correct!

I love how merge sort and heap sort sound better in theory (because quicksort has a worst case of O(n^2) while the others are always O(nlogn)) but in most applications not only they work at the same order but also quicksort gains by constants.

Excellent video, just used it in my class :))

I don't think Archimedes had access to trigonometry. You don't really show how you got your formula for going from 6 to 12 to 24 ... sides. I think this is a key step for understanding. Could you show where this came from? I do it a different way in my Archimedes pi video, but I would like to understand your method. (See ruclips.net/video/_rJdkhlWZVQ/видео.html for comparison.) Nice graphics. From other comments it sounds like you used a piece of software called Manim. Is that correct? I'll have to look it up.

Nice history lesson and excellent explanation of Archimedes' method for estimating the value of pi.

thank you

You need to talk much faster. When you sound like a mosquito, you will have achieved success.

damn that's so simple and beautiful newton is the true og

love me some quality content

how can you have 99.99% accuracy of a number that goes on forever? you cant even reach 1% accuracy of such a number.

Vey nice explanation. Loved the graphics. Thank you

Halley's method is Newton's method but uses the second derivative as well as the first and gives third order convergence instead of second.

You “ ran the simulation until either of the attacker or defender was completely wiped out”. The attacker can’t be completely wiped out, I assume you mean the attacker has one army left? And why would you run the sim with the presumption that an attacker with 1 die would attack a defender with 2 die or perhaps even 1 die? Cause you’d never make that attack in risk. It would be more informative to run your sim with the assumption that the attacker only attacks when it’s in his favour, which is anytime the attacker rolls more dice than the defender.

Excellent video! Thank you, although, I wonder why on the table you got from the millions of simulations, for the first confrontations i.e. (2;1), (3; 1), where (num att; num def), we do not get the same results as the plots you got statistically? For example, from the middle-bottom plot shown at 2:21, 2 attackers and 1 defender should lead to a loss of 1 for the defender about 57,5% of the time (and so a win for the attacker seeing as there is only 1 defender). But the table from the simulations shows it leads to an attacker win 75,4% of the time. Any idea why your simulations does not represent the statistical values for the confrontations with 1 defender?

We know that, the iterative formula to find bth root of a is given by: Xn+1 = ( (b-1)*Xn + a/(Xn^(b-1)) ) / b a=12 a^(1/6) = 1.513085749 1.513085749^6 = 12 12의 6제곱근 구하기 초기 x=1.513085749 로 잡았을 때, x = ( (5)*x+ a/(x^5) )/6 = 1.513085749 a=12 a^(1/2.5) = 2.701920077 2.701920077^2.5 = 12 x=2.701920077 x = ( (2.5-1)*x+ a/(x^(2.5-1)) )/2.5 = 2.701920077

X=(X+A/X)/2 X= Square Root ( A ) | X=A/X X= Square Root ( A )

감사합니다 😍😍😍

you are right, realistic car steering in games us really very difficult, thanks for the video.

great vid

great video, straight to the point

Can someone please explain to me how 3v3 for attackers is a slight disadvantage for the attackers. I understand that they might lose one of their dies but isn't every battle that starts with 3v2 advantageous for the attackers slightly? So it should have a domino effect as the numbers get better on both sides??

Show me ONE SQUARE OR CIRCLE OR A TRIANGLE ON EARTH ANYWHERE… There are NO SUCH shapes

Thanks for the video. The blog doesn't exist. Any suggestions for another site?

Thanks! I was looking for exactly that.

This is exactly what I was looking for. My wife and I recently played a game and it just went on and on and on until we finally just gave up. 😂 I started thinking about doing exactly what you just showed in this video. I’m happy I found it so now I don’t have to.

bad example, its not 0 both ends

Thanks!

hello, do you have an idea why I get pi with (1 + 1/-4.136866650678035)^-4.136866650678035 = 3.141592653589793 3488520084713809 ?? Thanks for your help and your usefull video about how to calculate pi :)

Working on an FPGA and I found the best general approximator is [(a+b) >> 1] for sqrt(a*b).

He trapped it using limits. In 400 BC! But no one calls his method limits. He did it again in the quadrature of the parabola.

The world's fastest computer based (java or C#) 'Newton's method' can be found by searching "NewtonPlus Square root".

Hm nice

Nice fun video. Just wondering, did you use AI TTS for narration? Some parts (like 3:55) sound a bit weird.

Like this video or you'll run out of Chat GPT quota

Finally someone who realizes that negative feedback control environments can be done with just 1 neuron 😁

Source Code pls

Thanks for this simple and awesome tutorial ❤

this is epic

Great work! Why do you believe it was developed by John Conway, tho? I'm pretty sure that's not true.

Oh my god I literally discovered this formula on paper using the average inequality an hour ago because I was just pissed off that my square root approximation program worked too slowly

2:22 women trying to park

Great tutorial - I am using it now to help my gf learn to park.

I programmed mine over the last few days...purely by accident. I started with 2 objects, one chaser and one runner. I then scaled that up...and a few hacks here and there and it's looking nice now...now I must continue my search for youtube videos about particle life!

Try to slow down a bit