

Title: Area Of a Circle Post by johhnywave on Mar 29^{th}, 2007, 10:45pm I put it into a picture because I don't feel like retyping it. http://img257.imageshack.us/img257/536/riddlemethisxy6.jpg Direct Link: http://img257.imageshack.us/img257/536/riddlemethisxy6.jpg Good Luck! 

Title: Re: Area Of a Circle Post by ThudanBlunder on Mar 30^{th}, 2007, 1:22am If the area of circle A is 3 times the area of circle B and the area of square WXYZ is 6 times the area of circle B then the area of square WXYZ is 2 times the area of circle A We know the area of square WXYZ is 4/http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/subpi.gif times the area of circle in square WXYZ So required ratio = 2*(http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/subpi.gif/4) = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/subpi.gif/2 

Title: Re: Area Of a Circle Post by srn347 on Sep 2^{nd}, 2007, 9:05pm Now try it with perimeter. 

Title: Re: Area Of a Circle Post by mikedagr8 on Sep 3^{rd}, 2007, 5:43am You should be able to do it. ;) 

Title: Re: Area Of a Circle Post by srn347 on Sep 6^{th}, 2007, 4:18pm Me or the uberpuzzler? 

Title: Re: Area Of a Circle Post by mikedagr8 on Sep 7^{th}, 2007, 3:30am Quote:
Well since your not an uberpuzzler.... 

Title: Re: Area Of a Circle Post by ima1trkpny on Sep 7^{th}, 2007, 2:22pm on 09/07/07 at 03:30:33, mikedagr8 wrote:
LOL... when he becomes uberpuzzler I will be totally depressed... I have yet to come across anything he hasn't answered with complete bogus. Really srn347, would it be too much to ask for you to show a bit of maturity? Though I may be asking too much from someone who is probably no more than 15 at the most... By the way Mike, nice avatar! :) 

Title: Re: Area Of a Circle Post by Aryabhatta on Sep 7^{th}, 2007, 3:50pm on 09/07/07 at 14:22:38, ima1trkpny wrote:
Now that you mention it, i thought those were burning buildings... but it actually says mikedagr8. Nice. 

Title: Re: Area Of a Circle Post by mikedagr8 on Sep 8^{th}, 2007, 2:14am on 09/07/07 at 15:50:43, Aryabhatta wrote:
Quote:
Thanks :D, srn347 is 13. Still, in certain religions like Judaism, he would be considered an adult, yet he has never shown it. It amazes me that he thinks he can cope with complex problems and ideas way over the top of his head, most of the time it is over mine aswell. It seems he has very selective hearing/reading. He doesn't even read problems, answers them and then runs away when confronted with insults and complaints. Quote:
He will never be an uberpuzzler in the way that I meant it. I won't deserve the title if I make that many posts, I just like to enjoy myself not post for the title. I did at one stage, but I have calmed down now. 

Title: Re: Area Of a Circle Post by Barukh on Sep 8^{th}, 2007, 4:12am on 09/08/07 at 02:14:57, mikedagr8 wrote:
You will become an uberpuzzler (by the rules of this forum) in a while, hardly 2 months after you joined it. ::) 

Title: Re: Area Of a Circle Post by mikedagr8 on Sep 8^{th}, 2007, 4:19am on 09/08/07 at 04:12:03, Barukh wrote:
Yes, but I don't deserve the title, rank maybe, but title no. I am not an uberpuzzler, If I were, well we can only imagine the possibilities. By this I mean, that 5 stars, maybe, being called an uberpuzzler, not at the moment. Look at flamingdragon. He was averaging 40 posts every 12 hours, he went from 150~  650+ in a few weeks if that. 

Title: Re: Area Of a Circle Post by ThudanBlunder on Sep 8^{th}, 2007, 4:54am on 09/08/07 at 04:19:08, mikedagr8 wrote:
And Iceman, whose posts often consist of of only one syllable, yes and no. Still, at least he contributes many WTF? type puzzles. But I think I am still the numero uno puzzle poster. 8) In terms of amount of lines posted [and helpfulness of posts], I would say that Icarus is #1, probably followed by towr. 

Title: Re: Area Of a Circle Post by mikedagr8 on Sep 8^{th}, 2007, 4:57am on 09/08/07 at 04:54:00, ThudanBlunder wrote:
And I would agree with you there. Although since Icarus has been away for several months now, I would bump you up to #2. If he ever returns (let's all hope he does), I would have to move you down. 

Title: Re: Area Of a Circle Post by ThudanBlunder on Sep 8^{th}, 2007, 5:14am on 09/08/07 at 04:57:21, mikedagr8 wrote:
Hmm....Grimbal might have something to say about that. 

Title: Re: Area Of a Circle Post by mikedagr8 on Sep 8^{th}, 2007, 5:16am on 09/08/07 at 05:14:11, ThudanBlunder wrote:
Equal second with Grimbal then. I mean, at least he has cool pictures everytime the page refreshes. 

Title: Re: Area Of a Circle Post by srn347 on Sep 8^{th}, 2007, 11:53am Your comments don't even deserve a response, but unfortunetly it takes a response to say that. 

Title: Re: Area Of a Circle Post by towr on Sep 9^{th}, 2007, 7:40am on 09/07/07 at 14:22:38, ima1trkpny wrote:


Title: Re: Area Of a Circle Post by Barukh on Sep 9^{th}, 2007, 10:33pm on 09/08/07 at 02:14:57, mikedagr8 wrote:
How do you know? 

Title: Re: Area Of a Circle Post by ima1trkpny on Sep 9^{th}, 2007, 10:42pm on 09/09/07 at 22:33:32, Barukh wrote:
I don't know how mikedagr8 knows, but it makes sense with his math level he just told me was advanced algebra (the equivalent of the U.S. Algebra 2) which would be possible if he was taking honors courses, etc (which would explain the overconfident, cocky attitude...) 

Title: Re: Area Of a Circle Post by towr on Sep 10^{th}, 2007, 12:26am on 09/09/07 at 22:33:32, Barukh wrote:


Title: Re: Area Of a Circle Post by mikedagr8 on Sep 10^{th}, 2007, 2:18am 70 riddles / hard / Re: Hard: 24 Aug 29th, 2007, 6:07am Started by ootte  Post by srn347 Quote:
Quote:
This guy really is a character. Remember, according to a 13 year old, who says he has done calculus, 0/0 is 24. ;) I mean, I don't start learning calculus for another year, but he has already learnt it, probably mastered it to his standards as well. 

Title: Re: Area Of a Circle Post by ima1trkpny on Sep 10^{th}, 2007, 1:26pm Really? :o Actually Mike I would have figured you had already started it... in fact you probably are already much closer than you think... at least in all the courses I had, you were learning the concepts and building the foundation ahead of time, they just didn't tell you as such. Then when you got to calculus they just went "suprise! now here is how to use it..." But you'll probably like it... it just makes so much sense you wonder why everyone gives it such a stigma. Good luck! ;D 

Title: Re: Area Of a Circle Post by mikedagr8 on Sep 11^{th}, 2007, 12:41am on 09/10/07 at 13:26:32, ima1trkpny wrote:
YES, THAT'S EXACTLY WHAT IS HAPPENING!!! Next topic we start derivatives....CALCULUS WOOOOH! We're doing circular functions, then on to 'rates of change' and 'differentiation of polynomials'!!! ;D :D 8) :o :) 

Title: Re: Area Of a Circle Post by Sameer on Sep 11^{th}, 2007, 8:55am Wait how can you start on derivatives without limits? Btw what is the thread about? 

Title: Re: Area Of a Circle Post by mikedagr8 on Sep 11^{th}, 2007, 2:35pm on 09/11/07 at 08:55:55, Sameer wrote:
Rates of change has a subchapter I suppose you would call it, with limits as a topic. It's a jumbled book, and the teacher teaches in his own methods so I guess we will see. This thread was just a general conversation/topic. I'm not 100% sure anymore :/ 

Title: Re: Area Of a Circle Post by Obob on Sep 11^{th}, 2007, 3:25pm Well you can do differentiation of polynomials without knowing about limits. You can't prove your answer is correct (not that you even know what correct means, since you can't define derivative), but at least you can differentiate them. Strangely enough, differentiation of polynomials is actually an important concept in algebraic geometry, which is a field of math where you can talk about curves and stuff over number systems other than the real or complex numbers, where there is no notion of limits. You simply define the derivative of the polynomial to be what you would expect it to be in the real or complex case. 

Title: Re: Area Of a Circle Post by Eigenray on Sep 12^{th}, 2007, 1:51am Here is an example of how differentiation can be useful, even though limits make no sense. You may know that a polynomial f(x) has repeated roots (over http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/bbc.gif, say) if and only if f(x) and f'(x) have a common (nonconstant) factor. That is, by applying polynomial division with remainder, you can perform the Euclidean algorithm to compute gcd(f, f'). If you get a constant, then f has distinct roots (f is separable). But in fact, this result holds with polynomials over any field F, if we compute the derivative formally. That is, if f(x) = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gifa_{k}x^{k}, define f'(x) = http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/sum.gifk a_{k}x^{k1}. The proof only uses that F is a field. One reason this result is useful is that one can show certain fields F are "perfect", which means any irreducible polynomial over F has no repeated roots, or that any algebraic field extension of F is "separable", which is an important concept in field theory. In fact, this is almost immediate if F has characteristic 0 (that is, it contains a copy of http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/bbq.gif): if f is a nonconstant polynomial, then f' is nonzero, and has smaller degree than f. If f is irreducible then, it can't have a common factor with f', and so f has distinct roots. But suppose F=http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/bbf.gif_{p} is the finite field with p elements, also known as "http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/bbz.gif mod p", or http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/bbz.gif/(phttp://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/bbz.gif) = {0,1,...,p1}. Then there are nonconstant polynomials whose derivative is 0. For example, if g(x)=x^{p}1, then g'(x) = px^{p1} = 0, even though g(x) is nonconstant (even as a function on F). On the other hand, if h(x)=x^{p}x+1, say, then h(a)=1 for all a http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/in.gif F, so is "constant" in that sense, even though h'(x) = 1. Now, since g'=0, g and g' share a common factor (namely g itself), so g has repeated roots. In fact, g(x) = x^{p}1 = (x1)^{p}. But if we were to view g as a polynomial over http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/bbq.gif, it would be separable. On the other hand, since h'(x)=1, it is relatively prime to h, so h has no repeated roots over F. The ability for f' to be 0 even when f is nonconstant makes characteristic p fields more interesting. Finite fields are still perfect, but many infinite fields aren't. Derivatives can be generalized even more, to any algebra A over a field F. An Flinear map d:A>A is called a derivation if d(uv)=d(u)v + ud(v). For example, if A=F[x], then d is uniquely determined by d(x); if d(x)=1, then d is the usual derivative. But in general, the set of all derivations on A is itself a vector space over F. This comes up in differential geometry, Lie algebras, and stuff. Ramble ramble. 

Title: Re: Area Of a Circle Post by DC1E2L on Oct 23^{rd}, 2007, 4:29am Officially started calculus, and have learnt a few things inc. limits as you guys said. And a few forms of the notation. Also the basics of derivatives. 

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