Tuesday, March 14, 2006

Pi stories

Apparently today, March 14th, is PI.-day (3.14, get it ?). Actually, as my Greek Calculus instructor once informed us, PI is correctly pronounced "P" (just like the equivalent English letter). [In a related story, a Greek physics grad student teaching assistant told me that he once got back evaluations from his students which said that he did a good job at everything except pronouncing the Greek alphabet correctly !]. But back to PI.

Not long ago I was called in to mediate a dispute between an 8-yr old girl (my cousin) and her mechanical-engineer father. My cousin's teacher had told her that if you wrote down the decimal expansion of PI, the sequence of digits would go on forever without repetition. Her dad then took out paper and pen and divided 22 by 7 and showed her that the digits did in fact repeat. I, of course, had to inform them that the teacher was right and that PI is only approximately equal to 22/7 and, in fact, is irrational (even transcendental) and therefore can not be expressed as an integer over another integer (in the process perhaps causing long term damage to the sacred bond of trust between father and daughter). I suspect the assumption that PI is exactly equal to 22/7 is more common among people who learnt math without calculators.

I'd like to say that I took out pen and paper and wrote out the proof of the irrationality of PI, but sadly they had to take it on faith. I did find it on the internet later though. Before I direct you to the proof, I hope you notice the time-stamp on this post. Getting the post in exactly at 3.14 1:59:26 was a complicated task involving synchronizing the clock on my PC to Blogger's clock and then making sure that the first key was hit just as the second digits turned to 26. Ok, here's the proof thanks to Helmut Richter.

8 Comments:

Anonymous Manoj said...

I remember how my Mom used to introduce her 7th standard students to pi. She made them all draw circles of varying sizes in their notebooks, get them to use a thread to measure the circumference and divide by its diameter. I guess she loved the look on their faces when they all reported the same number (approximately). I'm not saying it's an example of good teaching, but sure beats the way I was taught the same.

3/16/2006 01:54:00 PM  
Blogger ashvin said...

I think that is a very cool way to learn about Pi. Though they probably don't realize the full significance of that fact until when they look back later.

3/21/2006 08:11:00 AM  
Anonymous brimful said...

Good lord- I think this post succeeding in melting my brain. In a good way.

And I'm glad you're posting more regularly again!

3/21/2006 11:22:00 AM  
Blogger ashvin said...


Good lord- I think this post succeeding in melting my brain

:) Actually that's how I sometimes feel when I hear about oncogenes and protein receptors.

3/21/2006 06:44:00 PM  
Blogger tanvi said...

Can I just say that I LOVED the fact that you posted at a pi moment. It was truly brilliant! I am now quite disappointed in myself for not even thinking of that when I did my pi day post. As for pi being pronounced as 'p', I gotta say that is the first time I have ever heard that. I'll have the find my calc prof and demand an explanation.

3/22/2006 02:28:00 PM  
Blogger ashvin said...

Thanks tanvi, I'm glad somebody appreciated that :) I'll let you in on a little secret: you can change your blogger time-stamp so that your pi-day post is also time-stamped 1:59:26. Actually I couldn't figure out how to change the digits on the seconds. Let me know if you do.

Oh: and it's only the greeks that pronounce PI like 'p'. But I think they have a right to decide how it's correctly pronounced.

3/22/2006 11:26:00 PM  
Anonymous andrea said...

hmm... my seventh-grade math teacher in houston pronounced it 'paeh' like any good Texan should. it's all approximate anyway, right ? ;)

you are a nerd for writing a post on pi, doubly so for making your timestamp 3/14 1:59:26.

That means you are cool in my book.

3/29/2006 01:19:00 PM  
Blogger ashvin said...

you are a nerd for writing a post on pi, doubly so for making your timestamp 3/14 1:59:26.

That means you are cool in my book.


That's right; I'm a nerd and proud of it :)

3/29/2006 01:42:00 PM  

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