1/root 88 112 136 160 184 208 232 square 81 100 121 144 169 196 225 index 1 2 3 4 5 6 7 64 17 19 21 23 25 27 29 (256 1024)256 - 64 = 192 / (base root) 8 = 24We want the amount of squares in between 64 256 including 256 = 8 (always the root of course):So here are mapping offsets:For > 64….. and < 256:88 = 7 (always base power of 4 square (64) root = 8 -1 ) no math beyond getting the 7112 = 12136 = 15160 = 16 (always root * 2)184 = 15208 = 12232 = 7for > 256….. and < 1024:289 = 15 (always base root – 1) (don’t do math with this beyond getting the 15)xxxx etc. 576 = 64 (the root * 2)xxxx961 = 15The pattern seems to be, the first next perfect square after 64… = 8 – 1 = 7. Then + next odd number down (5) = 12 + NOD = 15 + NOD = 16. Then subtracts the same values back down to 7 for 232 (for square 225). ... continued.... for index 24 = root*2 (constant equation). so then 1/4 = 0.25 (=another constant) * index of 2 = 0.5 So then 7 + ((root=8)*0.5 =4) + (index – 1 = 1) = 12.for index 34 = root*2 (constant equation). So then (constant)0.25 * index of 3 = 0.75.So then 7 + ((root=8)*0.75 = 6) +(index – 1 = 2) = 15if linear index was 2, converted is 112 – 12 = 100If linear index 3, converted value is 136 – 15 = 121obviously you will eventually run out of decimal spaces for larger power of 4 square ranges. < 0.000125. You can make the numbers bigger, and then divide back down at the end to get correct numbers.Also, must account for fractions of higher ranges when indexing “in between” the normal , which is very easy. If you wanted 89 square: 1/spread (ie 100 – 81)=19 *( 89 -81) = 8 then iterate. Good seed.
forgot to mention - if you want > 4 index, you do index - 4, this gives you reverse values to go back down. Whereas usually it's 4 - index for < 4.I also want to make it clear the relative "4" position is always root*2. So between 64 - 256, that's 16. (8 * 2 = 16).256 - 1024 would be 32. (16 * 2 = 32).This "half way" point is ALWAYS Root*2.Also want to clarify that the linear divisions are ALWAYS in between the actual locations of the squares number wise. So it never overlaps.You also want to figure out which left or right linear divisions on either side of your input number is closer to.
yeah so this is kinda ground breaking. Throughout history people said it was impossible to calculate square roots without repeating/looping steps. I proved them wrong. This is the next level of square root calculations right here...
I'm not positive anyone knows what you're trying to communicate. Based on your description I have no Idea how I would attempt to use this method of yours.It is not coherent.
