Search found 153 matches

by Corei13
Tue Dec 18, 2012 2:23 am
Forum: Introductions
Topic: আবার দেখা!
Replies: 9
Views: 3187

Re: আবার দেখা!

কেমন আছেন আপু? :)
কোন ভার্সিটি PM করেন। :P
by Corei13
Sun Nov 18, 2012 3:40 pm
Forum: Computer Science
Topic: Calculate ln(x) without math.h
Replies: 7
Views: 3445

Re: Calculate ln(x) without math.h

Then write a function exp(x) to calculate (e^x) and use binary search.
by Corei13
Sat Nov 17, 2012 7:35 pm
Forum: Computer Science
Topic: Calculate ln(x) without math.h
Replies: 7
Views: 3445

Re: Calculate ln(x) without math.h

Use Maclaurin Series of ln(x).
by Corei13
Mon Nov 05, 2012 7:55 pm
Forum: News / Announcements
Topic: Active users for marathon
Replies: 23
Views: 6088

Re: Active users for marathon

Count me in too :P

And,
if ( forum.getInterestedMembers() >= enough && topic.found() )
{
timeToArrange( onlineCamp, me ) = enough; // :)
}
by Corei13
Tue Mar 27, 2012 9:39 pm
Forum: Algebra
Topic: Functional Equations PSet : From Very Basic
Replies: 3
Views: 1010

Functional Equations PSet : From Very Basic

Here are 50 Functional Equations ( and Inequalities ) from Mathlinks, various contests, own and including basic equations like Cauchy's, Jensen's and D-Alembert's. ( There may be some confusion with the definition of range and co-domain, Wiki says Range $\subseteq$ Co-domain, but somehow not only me...
by Corei13
Mon Mar 12, 2012 10:10 pm
Forum: International Mathematical Olympiad (IMO)
Topic: IMO-1983-6
Replies: 15
Views: 2820

Re: IMO-1983-6

এই বইয়ে এত বড় ভুল কেমনে করল :O
ওরা লিখসে other cases are similar, কিন্তু $a\le b \le c$ নে, তারপর ওরা যা করসে তা কর, ( মানে ওদের পুরা সমাধানে swap(a,c); ), দেখ সমাধান আসবে না। ওদেরটা ভুল :-(
by Corei13
Mon Mar 12, 2012 8:03 pm
Forum: International Mathematical Olympiad (IMO)
Topic: IMO-1983-6
Replies: 15
Views: 2820

Re: IMO-1983-6

পোলাপাইন, This is not a symmetric inequality but a cyclic one. So you Can't WLOG assume that $a\ge b\ge c$, instead you can assume WLOG either $a\ge b \ge c$ OR $a\le b\le x$. And, as it is not symmetric, you can't use Muirhead 's inequality.
by Corei13
Mon Mar 12, 2012 7:33 pm
Forum: Algebra
Topic: interesting fun eq
Replies: 3
Views: 902

Re: interesting fun eq

Denote the statement by $P(x,y)$.
$P(x,0),P(0,x)$ imply that $f$ is a Cauchy equation and $f(x^2)=xf(x)$
Now, $(x+1)(f(x)+f(1))=(x+1)f(x+1)=f((x+1)^2)=f(x^2 + 2x + 1)$
$=xf(x)+2f(x)+f(1)$
So, $f(x)=xf(1)$.
by Corei13
Fri Feb 24, 2012 10:47 pm
Forum: Geometry
Topic: (Maybe Very) Hard Geometric Inequality
Replies: 2
Views: 781

(Maybe Very) Hard Geometric Inequality

Let $\triangle ABC$ is a triangle with circumradius $R$. Extend $AB$ to $R$, $BC$ to $P$ an $CA$ to $Q$ and let $D,E,F$ be the midpoints of $BC$, $CA$, $AB$ respectively.
Prove that,
\[\frac{PQ}{AB}+\frac{QR}{BC}+\frac{RP}{CA} \ge \frac{PD+QE+RF}{R}\]
by Corei13
Fri Feb 24, 2012 10:45 pm
Forum: College / University Level
Topic: a problem from IUMO 09
Replies: 11
Views: 4181

Re: a problem from IUMO 09

What's your new problem? I couldn't get it. :(