## experimentX 3 years ago Happy $$\huge \pi$$ day!! prove $$\pi$$ is irrational:

1. anonymous

Did u mean to prove pi is a irrational number?

2. experimentX

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

3. anonymous

and i can evan type it in binary code

4. experimentX

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

5. anonymous

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

6. experimentX

In that case i'll change my question then.

7. anonymous

8. anonymous

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

9. experimentX

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

10. experimentX

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.

11. experimentX

but i does prove something really really nice ..

12. anonymous

and what is that?

13. experimentX

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

14. experimentX

a very nice geometrical interpretation ..

15. anonymous

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

16. experimentX

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

17. anonymous

i love pie but not pi

18. experimentX

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

19. anonymous

i dont know i have herd of that though

20. anonymous

i like pie lol

21. anonymous

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

22. experimentX

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

23. anonymous

i memorized the first 100 digits

24. anonymous

there is a whole lot more for me to memorize

25. experimentX

wow!!

26. experimentX

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

27. anonymous

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

28. experimentX

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

29. anonymous

brb

30. mathslover

Well it can be proved by contradiction.

31. experimentX

give it a try ...

32. mathslover

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!

33. experimentX

do you understand any one of those?

34. mathslover

Welll @experimentX that's a tough question!

35. experimentX

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

36. mathslover

37. mathslover

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

38. experimentX

a slight modification ...