Noir_Desir wrote:reminds me of my dad's easy way to do simple multiplications:
7*7? Just take 5*10 and subtract 1.
Curiously, the fact that 2 * 7^2 = 10^2 - 2 is connected to the digit pattern of sqrt(2):
Have you ever noticed that the pairs of digits are 2, 2, 3, and 5 times 7? and that the next two digits (62) are almost 9 times 7? The same pattern happens in sqrt(62):
Six digits per group this time, but the same 2, 2, 3, 5 ratio. This one is connected to the fact that 62 * 127^2 = 999998. Both roots get their digit patterns from the Taylor series expansion of sqrt(1/(1-2x)) :
I have written about this on my numbers webpage, but I can't post links yet so you'll have to Google or Bing it.
- Robert Munafo (I do love my numbers)