Bort - 2012-06-07
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.
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Adham Nu'man - 2012-06-08 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.
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TheQuakeSoldier - 2012-06-08 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".
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Adham Nu'man - 2012-06-08 Damn you Evan O'Dorney! DAMN YOU STRAIGHT TO HELL!
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Bort - 2012-06-08 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]
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Adham Nu'man - 2012-06-08 Damn you Bort! DAMN YOU STRAIGHT TO HELL!
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Mister Yuck - 2012-06-08 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.
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gambol - 2012-06-07
what's wrong with his mouth
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Adham Nu'man - 2012-06-07
His reaction to that final question is what made it for me.
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Squeamish - 2012-06-08
Who the hell wears a shirt like that.
You look like a fool, Evan. You look like a man grown in a religious catalog.
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Riskbreaker - 2012-06-08
Yeah but, can he finish Plataform Masters in less time than Uli? I DON'T THINK SO!
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TeenerTot - 2012-06-08
Yay maths!
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