Search found 16 matches
- Mon Aug 27, 2012 9:25 pm
- Forum: Combinatorics
- Topic: Sums
- Replies: 0
- Views: 1780
Sums
$n\geq4\in\mathbb{N}$. Prove that from any set of non-negative real numbers $x_1,\ldots,x_n$ with $x_1+\ldots+x_n\leq200$ and $x_1^2+\ldots+x_n^2\geq2500$, four numbers with sum at least 50 can be chosen.
- Tue Aug 07, 2012 11:04 pm
- Forum: Higher Secondary Level
- Topic: A rectangle in a Cartesian coordinate system
- Replies: 9
- Views: 7649
Re: A rectangle in a Cartesian coordinate system
$c=\min\{a,b\}<1$. To show that it's necessary, suppose $c\ge 1$. Then any square with side-length $c$ contains a point with integer coordinates. For sufficiency, consider any rectangle two of whose vertices are $(0,y)$ and $(0,y+c)$, with $y$ chosen so that $y+c<1$. This rectangle doesn't contain ...
- Wed Jul 25, 2012 4:38 pm
- Forum: Higher Secondary Level
- Topic: A rectangle in a Cartesian coordinate system
- Replies: 9
- Views: 7649
Re: A rectangle in a Cartesian coordinate system
Can you explain it alittle bit? It is too fast for me...
- Wed Jul 11, 2012 10:46 am
- Forum: Higher Secondary Level
- Topic: A rectangle in a Cartesian coordinate system
- Replies: 9
- Views: 7649
Re: A rectangle in a Cartesian coordinate system
Is anybody able to show the problem?
- Fri Jul 06, 2012 12:22 am
- Forum: Higher Secondary Level
- Topic: A rectangle in a Cartesian coordinate system
- Replies: 9
- Views: 7649
Re: A rectangle in a Cartesian coordinate system
If you rotate a square by $45°$ whose sides are a bit less than $\sqrt{2}$, it also doesn't contain a point.
- Fri Jun 29, 2012 4:32 pm
- Forum: Higher Secondary Level
- Topic: A rectangle in a Cartesian coordinate system
- Replies: 9
- Views: 7649
A rectangle in a Cartesian coordinate system
What are the necessary and sufficient conditions for the two numbers $a$ and $b$ so that it is possible to form a rectangle in a Cartesian coordinate system which does not contain points with integer coordinates?
- Wed Jun 27, 2012 12:39 am
- Forum: Higher Secondary Level
- Topic: For geometry lovers
- Replies: 6
- Views: 5263
Re: For geometry lovers
Nice solution!
- Tue Jun 26, 2012 12:22 am
- Forum: Higher Secondary Level
- Topic: For geometry lovers
- Replies: 6
- Views: 5263
For geometry lovers
Please look at the image.
$D$ is the image of a point reflection of $C_1$.
Prove: $CE=CB_1$
$D$ is the image of a point reflection of $C_1$.
Prove: $CE=CB_1$
- Mon Jun 25, 2012 7:31 pm
- Forum: Higher Secondary Level
- Topic: Residues
- Replies: 9
- Views: 6129
Re: Residues
Thank you very much!
- Mon Jun 25, 2012 6:51 pm
- Forum: Higher Secondary Level
- Topic: Residues
- Replies: 9
- Views: 6129
Re: Residues
The part (i) with a lot of dots.