Karim D. Ghantous
Well-known member
Every now and then I try to improve my knowledge of maths. I sometimes play with Grapher, the successor to Graphing Calculator. I discovered by accident something very interesting, if completely obvious to those who are more mathematically minded.
You would think that the square root of x squared would just be x, right? i.e. SQRT(x^2) = x. After all, taking the square root of a square is returning a number to its original value, right? Not so fast.
I'm not going to spoil it. But I am going to propose that this function has a practical value as a kind of number filter. Filter, you ask? You'll know what I mean when you plot it. If you're not sure how to plot it, it's y = SQRT(x^2). Now, compare that with y = x.
You can of course go further and replace x in any function with SQRT(x^2). E.g. sin x, tan x, etc. I don't know many equations but you get the idea.
You would think that the square root of x squared would just be x, right? i.e. SQRT(x^2) = x. After all, taking the square root of a square is returning a number to its original value, right? Not so fast.
I'm not going to spoil it. But I am going to propose that this function has a practical value as a kind of number filter. Filter, you ask? You'll know what I mean when you plot it. If you're not sure how to plot it, it's y = SQRT(x^2). Now, compare that with y = x.
You can of course go further and replace x in any function with SQRT(x^2). E.g. sin x, tan x, etc. I don't know many equations but you get the idea.