# User:Marco Polo

Jump to navigation Jump to search

## Friends

Stress Indicator

### Me

If Wikimedia had invented its "multi-login" setup before I had created this account, I would not be in this predicament, but alas, it was not to be. I am known under two (2) usernames. At the risk of being accused as a sock-puppeteer, I make this known here. The reason is that this username is taken on a few sister sites, so I use an alternate name there, but once the multi-login came about, My alternate obtained similarly-named accounts here and elsewhere. As a result, I now contribute using both users, as whim strikes me, but mostly my new one, since it does not have any name clashes. So look not here, but here for my recent contributions.

## A Proof that π really is irrational

Theorem: ${\displaystyle \pi }$ is irrational

By repeatedly applying integration by parts, the definite integrals of the functions ${\displaystyle f_{n}(x)\sin x\!}$ can be seen to have integer values. But ${\displaystyle f_{n}(x)\sin x\!}$ are strictly positive, except for the two points 0 and ${\displaystyle \pi }$, and these functions are bounded above by ${\displaystyle {\frac {1}{\pi }}}$ for all sufficiently large n. Thus for a large value of n, the definite integral of ${\displaystyle f_{n}(x)\sin x\!}$ is some value strictly between 0 and 1, a contradiction.

## Userboxes

Template:Babel Template:Babel
Userboxes that should have a template, but don't
 This user supports userboxes.
 POV This user supports userboxes that display points of view.
 This user scored 1036.5759155090532 on the Wikipediholic test (revision 59155841).

Template:Babel
My Website
 WEB This user has a website, which can be found at [http://unitedwebdesigners.awardspace.com United Web Designers]