Question

Challenge question:
Give a proof that Pi is irrational. (NO need to prove transcendental if not necessary)

Answer 1

proof by contradiction :)

Answer 2

proof by bandwagon

Answer 3

Let's assume that \(\pi\) is rational.\[\pi = {p \over q} \quad(\gcd{(p,q) = 1)} \]\[\pi q = p \]and now contradict.

Answer 4

Wait... I think I am going wrong.

Answer 5

I have to excuse myself- got to leave. MEDALS AND MENTIONS AND fan will be given TO anybody and everybody who CONTRIBUTES to the CORRECT answer

Answer 6

A number is irrational if:
1) It has infinite number of decimal numbers after the decimal.
2) It shows no pattern after the decimal(there are no repeating digits)

Pi possesses all the qualities shown above.

Answer 7

I don't think I am good at proofs. :(

Answer 8

the proof of irrationality of pi is not simple as other numbers
http://www.proofwiki.org/wiki/Pi_is_Irrational

Answer 9

\[\tan^{-1}x=x-\frac{x^3}{3!}.........\]
put x=1
we get
\[\frac{\pi}{4}=1-\frac{1}{3!}+\frac{1}{5!}-............................\]

Answer 10

wow. thats pretty nutty.

Answer 11

a friend of mine tried to formulate it using two concentric circles ... almost spent a week ... in the end he found that he was wrong.

Answer 12

was a good week though

Answer 13

crazy guy!!

Answer 14

Now we must proof that the series converges and we will have it

Answer 15

lol what?

Answer 16

nowdays there's a concept called rational trigonometry ... http://en.wikipedia.org/wiki/Rational_trigonometry ... quite different from it. though i don't understand it ... might be what you are looking for

Answer 17

This whole post is a waste of time. You know why? Because Pi is wrong: http://www.youtube.com/watch?v=jG7vhMMXagQ&feature=edu&list=PL5F03A9D6D278C5D9

Answer 18

Pi is not really wrong ... if it would have been replaced by tau then things would have been much simpler. well ... to me doesn't make much difference.

Answer 19

I think it can be proved with Taylor's series error, I saw a proof of e being irrational in Calculus I course with taylor's series.

Answer 20

wow tau owns.

Answer 21

man i have not that patience to read proofs about pi irrationality or e but sin 1 is better

Answer 22

eem of course e's proof is much simpler than pi

Answer 23

i forgot for sin(1) though ...

Answer 24

IT is proved that if x is non-zero and rational then this expression must be irrational. Since tan(π⁄4) = 1, it follows that π⁄4 is irrational and therefore that π is irrational.....

Answer 25

@mayankdevnai This is mcuh more elegant - only if the statement " if x is non-zero and rational then this expression must be irrational" can be proven though.

Answer 26

@mayankdevnani This is mcuh more elegant - only if the statement " if x is non-zero and rational then this expression must be irrational" can be proven though.

Answer 27

@Mikael oh!! i tried it by step by step...