WHAT IS THE SQUARE ROOT ALGORITHM? How does the square root algorithm work and why | Nathan Dalaklis
I go ahead and answer the question of 'what is the square root algorithm'. Before we look at this one of many algorithms from real analysis. I'll go through a sample computation and run through the square root algorithm steps without a calculator. After looking at the square root process and giving a nod to an intuitive geometric idea behind taking the square root, I will present a more rigorous version of the algorithm and with the help of the proof of the existence of square roots and the Monotone Convergence Theorem for Real Valued Sequences, provide a sketch of the proof for the algorithms limiting ability to provide the value of the square root of an arbitrary real number.
Skip to Geometric intiution: 5:20
Skip to Algorithm Breakdown: 6:51
_____________________
Last Video: • WHAT COMES AFTER CALCU...
The CHALKboard: / chalkboard
Find the CHALKboard on Facebook: bit.ly/CHALKboard
_____________________
#CHALK #RealAnalysis #Algorithms
Пікірлер: 39
Thank you for making this video. I learned the algorithm a few years ago, but I was never able to wrap my head around how and why it works.
@CHALKND
3 жыл бұрын
Glad it helped! 🙂
The way I did this in high school was using newtons method to "trace" parabola, just design parabola sothat x^2 - c = 0 and solve for x in an iterative manor.
@CHALKND
4 жыл бұрын
That is also the method that I learned in Highschool; I was never really completely happy with that approach (although I believe it is more efficient) since there are opportunities to miscalculate with Newton’s method.
That's really cool and I don't comprehend the proof at all. I love the algorithm.
@sovuchkin5093
2 жыл бұрын
I can't tell if you're being sarcastic or not
The intuitive description was great because allowed me think about it's generalisation to cubes and more.
@CHALKND
4 жыл бұрын
Just here reading comments foreshadowing a video planned for later this month.
Oh thanks a lot for this explanation. I've known this algorithm for years, and you gave me a light bulb effect to explain how it all makes sense! 🤯
Didn't have a clue what you are saying but I loved it so much that I wish if I could understand it!
Thanks for including the geometric interpretation, I absolutely love it when an explanation can be intuitive or realistic :D also, love the Salty Dog Cafe :P
Thank you ,I learned a lot
This was very interesting, thank you. Your presentation with chalk looks great.
@CHALKND
3 жыл бұрын
Glad you thought so thanks! 🙂
the math part was hard damn. but u showed the computation part pretty good. Probably after watching it again will understand it fully
Thank you for this I didn’t know an alg for square root
@CHALKND
Жыл бұрын
No problem glad you saw something new
I did actually find that hard to follow, and I have a 1st class degree in maths and computing. One thing you could do is make your writing bigger, and reduce the flurry of technical terminology.
My thought before the video: "why didn't i learn how to get square roots in school again" After the video: "oh yeah"
To be honest I know how to compute square roots of natural numbers,but can't understand the algorithm,they thought us how to compute square roots old school method like yours,thank you sir Chalk. How about cube roots of natural numbers and its algorithm 😃😎.
Say Nathan, you forgot about going to the old, old pre-calculator CDC tables.
how about taylor approximation?
8:25 Why didn't you deconvolve the original audio and apply the same point-spread function to match the acoustics of your patch you applied when you edited the video? Would it have delayed the release of the video? :-) Seriously, why doesn't _all_ editing software allow this stuff?
@CHALKND
4 жыл бұрын
Ah well, I am not skilled enough in audio editing to how I would even start to do the things you’ve listed here 😅.
@iangrant8174
4 жыл бұрын
@@CHALKND Oh! It's like this, but you use a z-transform, which is a discrete version of the Laplace Transform. kzread.info/dash/bejne/nIVtzNtvdri_mqw.html
I have a question, isnt it easier to guess and check method?
@CHALKND
5 ай бұрын
"Guess and check" methods of computation are highly dependent on the person's ability to estimate and complete simplified computations quickly. For some it may be faster.
@jiaxiang8017
4 ай бұрын
@@CHALKND Ok, thank you very much!
I did all this at school, but 66 years old now and none of it sticks any more!
Hello Chalk, why are you blinking So strongly?
@CHALKND
3 жыл бұрын
It is the way that an allergy I have is expressed. When I was little, my eye doctor was always fascinated by it.
@yasyasmarangoz3577
3 жыл бұрын
@@CHALKND cool ^^ I hope it does not bother you too much and that it was OK that I asked.
at 6:15 why are u telling two area will be 1/0.4 ...adding 0.4 to 1 (total 1.96 area=1.4^2) creates 3 measure area the one block just above the side 0.4 is 0.16 and the topmost two mini blocks having 0.4 each area . why 1/0.4? another thing 0.4 creates 0.16 area . and the remaining area is 0.8 as total is 1.96 measured so why the 0.8 block has been divided into two mini blocks at the top it could have been one block thats becoz if one block would be done it would not be a square it would become some what rectangle?
I only needed to watch like 4 minutes of this video to understand it
i hope your not a teacher.
@CHALKND
Жыл бұрын
👨🏻🏫
Thank you ,I learned a lot