Happy $ \huge \pi $ day!!

prove $ \pi $ is irrational:

Question

Happy $ \huge \pi $ day!!

prove  $ \pi $  is irrational:

anonymous · Answer

Did u mean to prove pi is a irrational number?

experimentx · Answer

Here is a simple way to prove that $ \pi $ is irrational using simple techniques of integral calculus. Who want's to try it on the occasion of $ \pi $ day

anonymous · Answer

and i can evan type it in binary code

experimentx · Answer

try to prove it's irrationality. not difficult if you follow the instructions given above image.

anonymous · Answer

im not good at irrationality i was trying to change the subject

experimentx · Answer

In that case i'll change my question then.

anonymous · Answer

attachment

anonymous · Answer

Now, if we can Prove 
lim n-->infinity sin(180/n) is irrational

experimentx · Answer

Nope ... that does not prove pi is irrational.

experimentx · Answer

it's the fundamental misunderstanding between limit and value of function. If you find limit of a function, it does not necessarily say that the function has that value.

experimentx · Answer

but i does prove something really really nice ..

anonymous · Answer

and what is that?

experimentx · Answer

sin(x)/x = 1 as x-> 0

experimentx · Answer

a very nice geometrical interpretation ..

anonymous · Answer

Pi is irrational because it never ends or repeats, right?

experimentx · Answer

it never ends ... <-- not just it
it never repeats (with above) <-- yes

anonymous · Answer

i love pie but not pi

experimentx · Answer

there was a Yahoo!! kid ... who loved Pie. I wonder where did he go???

anonymous · Answer

i dont know i have herd of that though

anonymous · Answer

i like pie lol

anonymous · Answer

pie is good and pi is 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 5920 78164 06286 20899 86280 34825 34211 70679

experimentx · Answer

how do you know so many numbers? don't tell me you've memorized all digits of pi

anonymous · Answer

i memorized the first 100 digits

anonymous · Answer

there is a whole lot more for me to memorize

experimentx · Answer

wow!!

experimentx · Answer

when it comes to memory, I am heavy as bag of hammers on a sea.

anonymous · Answer

same i just repeated it alot and it stuck in my brain

experimentx · Answer

i wish i could do that ... not pi but whole 100 theorems.

anonymous · Answer

brb

mathslover · Answer

Well it can be proved by contradiction.

experimentx · Answer

give it a try ...

mathslover · Answer

That can be found here : http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational I can not type the whole here.. It is too long!

experimentx · Answer

do you understand any one of those?

mathslover · Answer

Welll @experimentX that's a tough question!

experimentx · Answer

yes the proof of irrationality of pi is not simple. I found particularly this one understandable http://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational#Niven.27s_proof

mathslover · Answer

What about this ? https://pantherfile.uwm.edu/sboyd/www/m675s08/irrational_pi.pdf

mathslover · Answer

Oh .. It is the same that of Niven proof.

experimentx · Answer

a slight modification ...