Yes i Chat GPT'd my way into getting the formula but it still interests me about this topic. Click the green flag to start project. Click on character to skip.
This can be called the diamond root of the centered square root, either way both are correct. What is the diamond root? The diamond root of a number is the number of layers n needed to form a symmetrical diamond-shaped pattern using unit squares, where the total number of squares follows this rule. A diamond of root n has: drt(n)= 1+2n(n-1) This shape is formed by placing a single block in the center and surrounding it with layers that expand outwards symmetrically (in a diamond shape), increasing by 4, 8, 12, 16, 20, etc. squares per layer. Diamond Number Formula Give the diamond root n, the total number of unit squares is: drt(n)= 1+2n(n-1) Where: -drt(n) is the diamond number (total number of squares) -n is the diamond root (number of layers) Diamond Root Formula: If your given a diamond number n, you can compute the centered square root n using the inverse formula. n= (1+ sqrt(2n-1))/2 This formula is only valid if sqrt(2n-1) is an odd integer. Otherwise, n is not a valid diamond number Ex- Diamond Root n Diamond Number n 1 1+2(1)(0) =1 2 1+2(2)(1) =5 3 1+2(3)(2) =13 4 1+2(4)(3) =25 5 1+2(5)(4) =41 To reverse it: Diamond root of 13= (1+sqrt((2*13)-1)/2= (1+sqrt(26-1))/2= (1+sqrt25)/2= (1+5)/2= 6/2= 3 Anyways here's the formula to get the centered square root of any number: drt(n) = (1+ sqrt(2(n)-1))/2 Just replace the n variable with any number (That are greater than 0.5, otherwise you will get imaginary numbers.) and you will get it! c2a
