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#1 2005-10-02 03:11:59
- John E. Franklin
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square root accuracy
If a number greater than four is accurate to plus or minus 300%, what is the accuracy of its square root?
Oops, that's not what I meant.
If a number greater than four is accurate to multiply or divide by 4, what is the accuracy of its square root?
Last edited by John E. Franklin (2005-10-02 04:17:18)
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#2 2005-10-04 18:39:54
- abhishek_rttc
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Re: square root accuracy
Well, I don't understand exactly what u r seeking. But I'm still trying to help you-
let y=x^2
the log y = 2 log x
on differenciating
dy/y = 2 dx/x
Hence the accuracy % of a square root ( x in this particular case) should be 1/2 of the accuracy % of the number (y in this particular case) itself.
#3 2005-10-05 02:24:09
- John E. Franklin
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Re: square root accuracy
Thanks a lot abhishek_rttc! You have sparked my interest in calculus.
I knew the answer, but I couldn't prove it like you did! Neat.
The reason I am thinking about accuracy of numbers is because I wrote
a computer program recently that does +,-,*, and / out to 1000 or more
digits in the C language. And now I want to add significant figures and
plus or minus values to the input numbers and keep track of about how
far off the results are when you do multiple operations in a row. The
program calculated the cosine of 22 degrees to 200 digits, which was one
of my recent posts. Thanks again. If anyone wants a copy of the source
code, I'd be happy to present it, but I don't know what format is best.
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#4 2005-10-05 08:16:41
- MathsIsFun
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Re: square root accuracy
Hey, John, could't you do it in Javascript, so that you could enhance my Full Precision Calculator.
That way it can be used by everyone!
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#6 2005-10-07 02:07:35
- John E. Franklin
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Re: square root accuracy
I like programming in C and BASIC, and C compiled goes 5000 times faster than Just BASIC.
How fast is Javascript? Also I'd have to learn Javascript. And I don't claim to learn new stuff that
quickly. Also, the code that I write may not follow the standards you would be happy with.
I tend to use goto statements still. I like them better than "for loops" and "while loops" because you
can jump out of them without a "break" statement. And further, my program is still experimental,
but if you'd like to see it, you can do whatever you want with it, if you have the time. Or maybe
you could still convince me to learn Javascript. When I ran my C program to calculate the cosines
of ninety-one angles, using 120 iterations of a formula (120 terms). It took around five minutes
to finish, I wasn't timing it. After about 5 minutes, I had a file with cosines from 0 to 90 degrees.
I don't know much about number theory to know how accurate the series is at a given term, but I was
holding my calculations out to 500 places after the decimal for that run.
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#7 2005-10-07 07:51:28
- MathsIsFun
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Re: square root accuracy
Wow! Big stuff.
C is much faster than Javascript, but Javascript (or Java, it's big cousin) is very portable. I can write a Javascript and put it on the website and nearly everyone can use it straght away. With C, I would have to compile different versions for different operating systems, create a download and install process and then hope 
So it depends on what you want.
Anyway, Javascript is really easy (once you get past the wierd way you have to interact with the web page).
BTW I am not even very good at javascript (I am better at C, Visual Basic, SQL), but it's syntax is pretty standard, perhaps even a little too simple.
But once you write a few scripts and people start using them you start thinking "hey, it's pretty useful!"
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman