Talk:Proof that 22/7 exceeds π

"The following argument will be readily understood by persons with no knowledge of mathematics beyond first-year calculus. "

Well, what about those of us who don't even have that? It's all just funny looking symbols to me :) Adam Bishop 03:25, 29 Nov 2003 (UTC)

Well, "simple" is a subjective term. I don't think its possible to give a simpler proof than this, because even defining π involves calculus (the length of a curve is the limit of a sum, an integral). -- Arvindn 03:52, 29 Nov 2003 (UTC)

I suspect that any reasonable proof of the same proposition that avoids knowledge of calculus would be more complicated. As for calculus being involved in defining π, if someone who knows no calculus asks me what π is, I would not hesitate to answer that it is the ratio of a circle's circumference to its diameter; multiply the diameter by π to get the circumference. Michael Hardy 21:26, 29 Nov 2003 (UTC)

Do you know a (formal) definition of circumference that doesn't involve integration? If not, what I said still holds, doesn't it? -- Arvindn 03:27, 30 Nov 2003 (UTC)

It can be formally defined in terms of the limit of circumferences of polyhedra. This does need the notion of a limit, but not the fully machinery of integral calculus. However, since the formalization of the limit was done precisely to facilitate the development of calculus, the distinction is perhaps not a strong one in the history of formalism. However, in the history of Pi the earliest estimates of Pi make informal use of limits, but not of integration. (BTW, thanks for the name change from A very elementary...) ~ Jeff 18:33, 1 Dec 2003 (UTC)

Many characterizations of π do not mention integration. Which among them should be considered definitions is perhaps a subtler question. The notion of limit is not really needed, since one can say simply that it's the least upper bound of the set of all perimeters of inscribed polygons. Michael Hardy 21:40, 1 Dec 2003 (UTC)

If we use the continued fraction as definition, the proof is even simplier!!!wshun 21:49, 1 Dec 2003 (UTC)

How can the continued fraction be used as a definition? Somehow, you would have to say which continued fraction you're talking about without relying on some prior characterization of π. Michael Hardy 21:55, 1 Dec 2003 (UTC)

To elaborate a bit further on the point above: It is not as simple to understand how it is known that π = 3.1415926535... or that π = a certain continued fraction, as it is to learn calculus and then read this Wikipedia article. Michael Hardy 01:12, 2 Dec 2003 (UTC)

So, where does one go to brush up on the fact that integrating 1/(1 + x²) yields arctan? I had added a link to a page that included the formula, but it was removed. ~ Jeff 03:23, 4 Dec 2003 (UTC)

I suspect there may be a page that covers it, but I will add it to trigonometric substitution. Some of the calculus pages on Wikipedia have lots of problems. Michael Hardy 20:52, 4 Dec 2003 (UTC)

Thanks. Jake

So how many edges would a regular polygon (centre O, vertex V, edge bisector P) need before the ratio of the perimeter to OP was less than 22/7 ? That proof would not require caluclus, nor even limits, but only trigonometry. mike40033 03:01, 2 Apr 2004 (UTC)

oops. I meant, the ratio of the perimeter to 2*OP should be less than 22/7. Anyway, the answer is n=91. Using n = 96 and only trigonometry should yield a proof (with no calculus) that pi is less than 22/7. But I don't think the proof would count as "simple"

title

the title of the page says π , not π , somebody should fix that!

I've change the name to "A simple proof that 22/7 exceeds Pi" hopefully I changed all the links correctly ;-) Paul August 21:14, Jul 23, 2004 (UTC)

And now I've moved it to "a simple proof that 22/7 exceeds pi" (with a lower-case "p" in "pi") as a compromise. Until a couple of days ago, the π in the title looked like the lower-case Greek letter. I don't know why that changed. I'll look into it. But probably not today. Michael Hardy 23:53, 23 Jul 2004 (UTC)

I disagree with the title - its meant to be ironic. It should be obvious that ironic titles are not NPOV.-SV

I don't think the title is meant to be ironic. Why do you say this? Paul August 11:18, Jul 25, 2004 (UTC)

:) -SV

I suspect that he is thinking of the word "simple", because the proof isn't simple if you don't know any mathematics (see above). Pcb21| Pete 12:18, 26 Jul 2004 (UTC)

I suck reely bad at numbers and stuff, so I think your page should be named more simpler, no offense, but it makes the reader feel stupider than I think I is. -SV

It is a tricky one because the page plainly isn't simple if you are not mathematican (so don't feel bad Steve :)), however the reason for the pages existence is that it proves something about pi without relying on "heavy machinery" (at this point you kinda have to take it on trust that despite appearances all the machinery is fairly lightweight. And without some suitable adjective (we had elementary before, but that evokes the same probs as simple) in the title this raison d'etre gets lost. I vote that we merge into pi then the problem goes away. Pcb21| Pete 17:34, 26 Jul 2004 (UTC)