Discussion in 'Computer Science & Culture' started by Xelios, Dec 20, 2001.
Your source was wrong.
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Its quite possible that my source could have been wrong...
Pi is not the quotient of two integers; it's not 22/7 or any other quotient of integers. A number that is not the quotient of integers is called an irrational number. So pi is irrational. But a number that is irrational and is not the root of any algebraic equation is called transcendental. Pi is transcendental.
There's a simple proof, due to the Greeks - Euclid, I think - that the square root of 2 is irrational. You might want to look that up.
you said that pi is a number which does not contain recurring decimals and that it is infinite, i've heard that the number pi is infinite from some other people as well as you but i was thinking that since they havent calculated the exact value of pi, how do they know its infinite and dont have recurring digits at the end? who knows, imagine one day we'll find a fraction that number lol
btw, is the number pi calculated by circumference/diameter or circumference/radius? i forgot Please Register or Log in to view the hidden image!
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Aerosimon, take a number X = 0.55…. multiply it by 10 to get 10 X = 5.55… Now subtract X from 10 X to get 9 X = 5.0 Divide both sides by 9 to get X = 5/9 = 0.55…
A very similar process allows one to convert any repeating series of decimals to a ratio of integers. Proving pi is irrational is a little harder.
As for your second question… Picture a circle with diameter 1. Now imagine the diameter is a made of rubber and pull the center point of the diameter to the edge of the circle. Consider how much the diameter has to stretch. Not even close to three times right? Closer to 1.5 times. Now stretch a few more points from the “diameter” line to touch the circumference. Not much longer and now it’s following along half the circumference. (Opps...let's get it right this time. Hehe.) So half the circumference is close to 1.5 times the diameter. The circumference equals pi times the diameter. If you imagined all this you should have a way of remembering this formula. You’ll also have a good idea of how the Greeks calculated the value of pi.
It can be proved that pi is an irrational number (i.e. that it cannot be written as a fraction). The proof requires some complicated mathematics, which I can't teach you in this thread. But all mathematicians accept that the proof is valid.
This means we don't need to calculate pi to know it is irrational.
ok thanks for the info Imahamster and James R. lol James, even if you did show me the mathematics involved to prove that pi is irrational i dont think i'd understand it Please Register or Log in to view the hidden image! . maybe one day but definetely not now Please Register or Log in to view the hidden image!
Excuse me...is this Computer Science forum?
erm...may be i tumbled on to a wrong place.as i told Porf,that we need a Math forum to satisfy our mathematical itches,i am sure untill then people will continue to Bash computer science forums for that purpose... Please Register or Log in to view the hidden image!
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You'd be surprised at how much computer <b>science</b> is tied up with maths, one way or another.
As i pointed out earlier,any Science is incomplete without Maths...
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