So it seems like, if you want the square root of 45 (about 6.7082), you start out with a guess or approximation, let's say 6 (because the answer's somewhere between 6 and 7). So start with:
f(x) = (6x + 45) / (x + 6)
f(6) = (6*6 + 45) / (6 + 6) = 6.7500
Next iteration, keep the same function but with x = 6.75:
(6*6.75 + 45) / (6.75 + 6) = 6.7059
I am guessing that the slow version would be to change the function on each pass, so it would become:
(6.75*6.75 + 45) / (6.75 + 6.75) = 6.7083
Damn smart fella. I'd let him steal my lunch money.
Helo kids, uhhhm... if, you, uhhhm... find human emotions and social interaction, uhhhhhm.... confusing... uhhhhm... and nonsensical.... uhhhhhm... and that, uhhhhhhm... scares you a little... uhhhm.... then you probably find comfort in patterns, and... uhhhhhhm... maths has lots of comforting patterns.
Sorry to burst everyone's bubble, but that formula was invented by the BABYLONIANS like 3000 years ago. It's literally the first ever approximation of a square root ever conceived.
The Babylonian formula:
f(x) = 1/2 * (x + S/x)
and then rearranged....
= 1/2 * (x^2/x + S/x)
= 1/2 * ((x^2 + S) / x)
= (x^2 + S) / 2x
= (x * x + S) / (x + x)
The formula he just "invented".
Damn you Evan O'Dorney! DAMN YOU STRAIGHT TO HELL!
That's it, I'm getting my lunch money back.
... Waaaiiit, now I feel like I've really been cheated. Let's say we want to find the square root of S, and our first guess is x, and let's also say S/x = y. So if x is below the actual square root, y is above the actual square root, or vice versa. All this approximation is doing is splitting the difference between x and y. Sensible enough, but this is like finding out the magician didn't really steal your nose, that was actually his thumb. [SPOILERS]
The kid never claimed to have invented a new way to approximate square roots. He said found some formula to relate the existing fast method with an existing accurate method in a novel way that probably has implications us liberal arts majors can in no way comprehend. Or it's cool in some way that only the other aspies at Intel understand.
what's wrong with his mouth
|Adham Nu'man |
His reaction to that final question is what made it for me.
Who the hell wears a shirt like that.
You look like a fool, Evan. You look like a man grown in a religious catalog.
Yeah but, can he finish Plataform Masters in less time than Uli? I DON'T THINK SO!
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