Just one thought (before even finishing the video): Man you never fail to prove yourself (at least to my humble mathive self) as legendary as 3B1B and Numberphile here on YT. i remember i once embarked on a lonely journey to find out why this works, and sure got many lovely insights along the way; that's why i personally see how elegantly you nailed it. Well done.
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.
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.
You ought to see what doing this on binary numbers does! You do it the same way, pairing digits up. For the doubling, that simplifies to appending 0 to the right end. For the multiply & test, there is only 1 test: a 1 digit. You append 1 to right of the doubling. You multiply by 1 (don't need to do as it is the same number), do the subtract, discard if too large & append 0 to answer, else append 1 & keep the subtract. So for the test, you take answer (so far) & append "0 1" to the right of it, subtract, append either 0 or 1 to the answer, etc. A few iterations of square root of 2 illustrated. 1 . 0 1 1 √10.00 00 00 00 01 < first subtraction 1 00 < remainder, bring down next 2 digits 1 01 < this is answer with 01 appended, too large, discard difference, next answer digit 0 1 00 00 < unchanged remainder, bring down next 2 digits 10 01 < answer with 01 appended, not too large, next answer digit 1 01 11 00 < remainder subtracted from, bring down next pair 1 01 01 < answer with 01 appended, not too large, next answer digit 1 etc.
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
seems that there is a much clearer way to explain the maths visualization of the sqrt long division algorithm but thank you for this vid, and your interest in the subject
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.
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 😃😎.
Cube root (CR) is well explained on utube at "Crystal Clear Maths, Long Division Method for Cube Root". You will find it much more complicated than sqrt, but you can, if interested figure out a way to make it much more concise For instance I have figured out an algorithm which lets me find the CR of any number to 10 digit accuracy using only 2/3rds of a sheet. Taking 16 to 20 minutes. No separate worksheets, no erasing, no calculator help before or during. Most people would declare that this is impossible I even demod that I can find the CR of any number to 25 digit accuracy on 1 side of one standard sheet, using my improved long division algorithm for CR. That one takes around 2 hours, and requires optimum usage of your paper space
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 Oh! It's like this, but you use a z-transform, which is a discrete version of the Laplace Transform. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-jQ9jy6FUYjI.html
"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.
@@CHALKND For myself, I have always found that it is much clearer to just, in every iteration simply multiply the current root (a) by 20. (so, 20a) Using that, estimate your next digit (b) by mental division into the current remainder. Add your new digit to the 20a, multiply by b You basically did just that, but I have always found my procedure a bit clearer
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?
