Search found 186 matches
- Sun Feb 01, 2015 7:22 pm
- Forum: College / University Level
- Topic: Integrability
- Replies: 3
- Views: 10832
Re: Integrability
1. If a function doesn't "have" indefinite integral , then it doesn't "have" definite integral too because they are both same thing except the constant gets cancelled in definite integral and we get a definite value for 2 given limits . Now some functions (like $\ln(\ln x),x^x,\sin(\sin x)$ ) can n...
- Fri Dec 19, 2014 11:57 am
- Forum: Geometry
- Topic: Side, Angle, and, (Ex)-Circle
- Replies: 4
- Views: 4008
Re: Side, Angle, and, (Ex)-Circle
$O$ is the centre of the excircle opposite to $A$ , to match with notations used in books , $O=I_A$
- Tue Dec 16, 2014 7:07 pm
- Forum: Social Lounge
- Topic: Asking for a book
- Replies: 3
- Views: 3946
Re: Asking for a book
College Geometry by Nathan Altshiller-Court.
I haven't gone throughly this one , but I liked the contents , they cover nearly all important and useful things I suppose .
I haven't gone throughly this one , but I liked the contents , they cover nearly all important and useful things I suppose .
- Fri Dec 05, 2014 4:14 pm
- Forum: Junior Level
- Topic: A surprising problem!!
- Replies: 2
- Views: 3397
Re: A surprising problem!!
This may help you !
- Tue Nov 25, 2014 3:22 pm
- Forum: Geometry
- Topic: powers are equal
- Replies: 3
- Views: 3291
powers are equal
$P$ is inside $\Delta ABC$ such that $AB,BC,CA$ are tangents to the circumcircles of $\Delta BPC,\Delta CPA,\Delta APB$ respectively . Extended $AP,BP,CP$ cuts the circumcircle of $\Delta ABC$ at $A',B',C'$ . Prove that power of $A$ (with respect to $\odot B'PC$ ),power of $B$ (wrt $\odot C'PA$ ),po...
- Sat Nov 08, 2014 10:10 pm
- Forum: Physics
- Topic: Errors in Galileo’s Thought Experiment?
- Replies: 2
- Views: 4226
Re: Errors in Galileo’s Thought Experiment?
Logic isn't limited in common sense , it's process of applying principles which are known as truth . Yesterday's invention comes today handy for logicing . As I'm not a professional or even studied to that level yet , I have little experience regarding to scientific theory background . If logic shou...
- Sat Oct 25, 2014 5:04 pm
- Forum: Secondary Level
- Topic: A circle through incenter
- Replies: 2
- Views: 4616
A circle through incenter
In $\Delta ABC$ , the incircle touches $AC,AB$ at the points $E,F$ respectively . $M$ is the midpoint of $EF$ . A circle $\omega$ (center $O$ ) is drawn through incenter $I$ and $M$ . Prove that $IO$ and $EF$ meet on the circle $\omega$ .
[edited. Thanks to Sowmitra .]
[edited. Thanks to Sowmitra .]
- Tue Mar 04, 2014 12:43 pm
- Forum: Geometry
- Topic: Secondary Special Camp 2011: Geometry P 3
- Replies: 3
- Views: 3718
Re: Secondary Special Camp 2011: Geometry P 3
Zzzz via,you wrote:$\frac{BD}{CD}\times \frac{CE}{AE}\times \frac{AF}{FB}=1$.So,D,E,F collinear.Why! Here he used Menelaus' theorem , a theorem to prove collinearity . If three points lie on the three sides of a triangle (or their extensions) and are collinear , then they have this fraction relatio...
- Mon Mar 03, 2014 11:08 pm
- Forum: News / Announcements
- Topic: ২০১৪ আঞ্চলিক পর্যায়ের প্রশ্ন
- Replies: 4
- Views: 11387
Re: ২০১৪ আঞ্চলিক পর্যায়ের প্রশ্ন
আঞ্চলিকের প্রশ্ন দেওয়াটা হয়তবা একটু বেশি সমস্যার যেহেতু প্রব্লেম বেশি । তবে জাতীয়রগুলা দেওয়া যায় । বিক্ষিপ্ত ভাবে টপিক না করে সবগুলা একসাথে দেওয়া অনেক সহায়ক । তাছাড়া অনেকেই থাকে যারা কিনা অংশ নেয় নাই , কিন্তু প্রব্লেম জানতে আগ্রহী , তারা ফোরাম থেকে নিতে পারে । (যদিও অলিম্পিয়াড সাইটে প্রশ্ন...
Re: x,y,z>1
that was cool 8-) Let $x=a^2+1 , y=b^2+1 ,z=c^2+1 $, ($a,b,c>0$) then inequality becomes $\displaystyle \sqrt{a^2+b^2+c^2+3} \geq a+b+c$ $\Rightarrow a^2+b^2+c^2+3 \geq a^2+b^2+c^2+2ab+2bc+2ca$ $\Rightarrow \frac{3}{2}\geq ab+bc+ca $ We have $\sum \frac{1}{x}=2 \Rightarrow \sum \frac{1}{a^2+1}=2$ Le...