What Is Your Favourite Proof That.....

[ToraToraTora]

....πR² is the area of a circle. There are many, some more elegant than others. I recently learnt a new one that is probably old hat to the mathematicians on here but I loved its elegance. I'll say later if anyone gets it.

[237SJ]

Did the pubs chuck out early tonight?

[ToraToraTora]

its seems they did 237!

[Buenchico]

Abraham bar Hiyya utilised Archimedes' proof to provide his own, which must surely be one of the most elegant ever:

[237SJ]

I did wonder if you had been on the Worthington bitter

[ToraToraTora]

Bitter, is what poor northerners drink!

[237SJ]

When I was at college and working behind a bar we had a shortage of beer so we connected all of the beer pumps to the same barrels. Worthington E as I remember. Nobody noticed any difference.

[ToraToraTora]

yep that's the one Chico, I got it from Eddie Woo but essentially the same one. So obviously correct, and really simple yet who of us would come up with that alone.

EW's videos are usually less than 10 minutes and explain something you know, yet do not know WHY? I know most of the maths yet he's filled the "why" gaps that I didn't know that your teacher didn't tell you, or quite often didn't know themselves. Wonderful.

[ToraToraTora]

yep that was the early technique 237, E was the one!

[237SJ]

And we used to have a miserable old scrote that used to do the washing up in the pub. He was always on the scrounge for beer so one night we collected up the dregs from the pumps, put them in a pint glass and gave them to him. He said they went down a treat.

[ToraToraTora]

....tomorrow we are doing why fractional powers are roots, watch this space.

[237SJ]

I hope you're not to 'tired' in the morning

[237SJ]

*too*

[ToraToraTora]

Why would I be? not everyone gets peeced on saturday, some of us are drunk with knowledge. I find maths intoxicating I'm studying more and more these days.

[THECORBYLOON]

If you cannot wait until to-morrow, see the answers here,

https://math.stackexchange.com/questions/1366082/why-is-a-fractional-exponent-a-root

The first answer is more straightforward than the second.

[douglas9401]

Looks like the square of the hypotenuse has nodded off.