# Having a little fun with the basics tonight **URL:** \ **Category:** Mental Calculation, Mathematics, and Puzzles\ **Created:** [July 19, 2019, 1:38am UTC](https://forum.artofmemory.com/t/having-a-little-fun-with-the-basics-tonight/40042 "2019-07-19T01:38:28Z")\ **Posts on this page:** 1\ **Showing post:** 8
**Author:** ![Kinma](https://forum.artofmemory.com/letter_avatar_proxy/v4/letter/k/a88e4f/32.png) [@Kinma](https://forum.artofmemory.com/u/Kinma)\ **Post date:** [July 22, 2019, 3:06pm UTC](https://forum.artofmemory.com/t/having-a-little-fun-with-the-basics-tonight/40042/8 "2019-07-22T15:06:06Z")
> [@zvuv](#): > > I, developing a modified decimal system to represent numbers. Instead of confining each power of ten to a single column with a single digit, they are marked by commas which allows one overflows and also -ve numbers. This is a fantastic method and I advocate using this highly. On this forum I already use this, for example here: > [@Duplex method for squaring numbers very quickly](https://forum.artofmemory.com/t/duplex-method-for-squaring-numbers-very-quickly/32822): > > The speed the Indians calculate at the mental calculation world championships is ridiculous. I mean this in a positive way. Unbelievable! Here is an example of the current world record holder Shashank Jain taking 10 square roots just a little over 1 minute: [https://www.youtube.com/watch?v=ktFX7Lkr4rk&t](https://www.youtube.com/watch?v=ktFX7Lkr4rk&t) Nodas explained in a separate post [https://artofmemory.com/forums/granth-thakkars-world-record-for-20-digit-multiplication#comment-33683](https://artofmemory.com/forums/granth-thakkars-world-record-for-20-digit-multiplication#comment-33683) that they do this using the duplex method and if you t… > [@Help choosing a system for mental math](https://forum.artofmemory.com/t/help-choosing-a-system-for-mental-math/32751/6): > > Exactly. And as a future engineer, I find it to be a very attractive facility to have. The techniques even lend themselves to integration. After plugging in the limits of integration, mental math could make the evaluation process very quick (I imagine). That was my suspicion. You said that you would recommend that I memorize squares. How far up should I memorize them? I read somewhere that 30 is a good point. Would you agree? That makes sense. Calculate squares using shortcut methods, then… > [@Duplex method for square roots](https://forum.artofmemory.com/t/duplex-method-for-square-roots/32913): > > In a previous [thread](https://artofmemory.com/forums/duplex-method-for-squaring-numbers-very-quickly) I talked about the duplex method for squaring numbers. Read that first if you have no idea how this method works. Otherwise; you might not understand this thread. If you can square numbers using duplex numbers, then taking the square root is just working backwards, which we will do here. Let’s go forward first and then backward. This will make the calculation clear. 857^2 = 64 | 80 | 137 | 70 | 49 = taking care of carrying: 72 | 13 | 14 | 4 | 9 = another round: 73 … Instead of a comma, I use the | character (vertical bar) which I find makes for better reading. And indeed it has lots of advantages, like better carry handling. Realising that 69 can be written as: 7 | -1 makes for much easier multiplication, like I wrote about here: > [@General discussion of mental maths](https://forum.artofmemory.com/t/general-discussion-of-mental-maths/28679/22): > > Criss cross using [negative values](https://artofmemory.com/forums/avoiding-the-carry-5494.html): 90 -1 50 -3 \_\_\_\_\_\_\_ X 90X50 = 4500 (-1 X 50) + (-3 X 90) = -50 - 270 = -320 -1 X -3 = 3 \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ + 4500 -320 (=4180) -+3 (=4183) Anchor method using 50 as anchor: 1st step. We add 3 to 47 to get 50. Therefore we subtract the same 3 from 89 to get 86. Now multiply them: 50 X 86 = 4300 Now subtract the difference from the base numbers (we changed 47 into 50 and 89 into 86. So difference is 3) and multiply by the distance… > [@zvuv](#): > > Breaking free of the tyranny of the columns allows us to keep partial results in their original form as long as we wish and it allows us different ways to represent the same decimal number which can preserve structure that gets flattened by the column system. Exactly! --- _[View the full topic](https://forum.artofmemory.com/t/having-a-little-fun-with-the-basics-tonight/40042)._