Problem Searching and Naming!

**Posted:** Thu Dec 23, 2004 11:43 am

_________________
Math is like love. A simple idea but it can get complicated.

1000 · New Member Offline Joined: 08 Jun 2004 Posts: 7

Here is my solution to this problem:

First we need to catagorize all the old inequalities, so a user can easily see if the inequality he/she wants to post already exists or not.... So here are the important catagories:

1. Inequality Class - First he/she defines the class of inequalites this inequality belongs to: is it algebraic, trigonometric, geometric, number-theoritic/combinatoric (ex. 1*3*5*...*(2n-1)<n^n)

2. Inequality Sign- What type of sign does the inequality have >, >=, >> ?

3. Number of Variables- How many variables does it have:
1( inequalities like x^6+2 >= x^4 +2x), 2, 3, 4, 5 or n-variables?

4. Type of variables? Do the variables belong to the set of integral, non-negative, real or complex numbers? etc.

5. Type of Inequality- This is the most important catagory, after the user replies to catagory 1 and 3, they can then select the type of inequality it belongs to: For example if an inequlity is algebriac and has 3 variables, the user can select from the list below to narrow the search:

a. Symmetric Inequality- ex. a + b + c > abc.
b. Inequality with Roots- ex.
$\displaystyle x^2+y^2+z^2+\sqrt\r\n{3xyz(x+y+z)\r\n}\geq2(xy+yz+zx)$
c. Inequality with Fractions- ex.
$\displaystyle \displaystyle \frac{a^3}{2a^2+b^2}+\frac{b^3}{2b^2+c^2}+\frac{c^3}{2c^2+a^2} \ge \frac{a+b+c}{3}$
d. Power Inequality- Inequalites where the variables are powers. Ex.
$\displaystyle \\ac^b+\frac{b}{c^a}\geq a+b$

etc.

6. Constraints/Conditions - To help narrow down the search the user can select what types of conditions the problem has, for example for an algabraic inequality with 3 var. we can have a + b +c =1, or a + b +c <=1, or abc=1, or abc<=1, or a+b<c, or another inequality, etc.

7. Origin of the Inequality- Is the inequality from the IMO? AMO, BMO, CMO, ... etc.
or is it from journals? ... etc.

In all I think these 7 catagories can narrow down the inequality correctly. But this requires a lot of time to go through all the old inequalities. Further, I recommend we set rules on variables... for example for all 3-var. algabraic inequalities we have to use only the variables a, b, c. So that the search engine can easily match equations. I hope this well help.

**Posted:** Mon Jan 17, 2005 12:21 pm

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1000 aka. $10^3$

manlio

It is a long job Confused

**Posted:** Mon Jan 17, 2005 1:27 pm

orl

**Posted:** Tue Jan 18, 2005 3:22 am

_________________
Math is like love. A simple idea but it can get complicated.

Megus

As nothing was done yet why not to do something that was mentioned [unfortunately I don't remember who mentioned it] in some other topic. I mean: create additional subsection in every Olympiad Section subforum (essentialy in Inequalities Smile

) where all the famous problems would be stored (like Iranian 1996 ineq, etc). It'd rather won't help in bringing the order (proper naming of the problems Smile

), however it'd be easier to find particular links.

**Posted:** Sun May 01, 2005 6:03 am

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Przemyslaw Chojecki

harazi

Well, I have still one week of holidays and after that I won't be able to help. But if there is anything to be done in this issue this week, I'm ready. You know, I think it is a little bit ridiculous to see each time the same problem and to post each time the same solutions. If there are different solutions, ok, but most of the time they are all the same. So, why shouldn't we put in a special place all popular or difficult or nice or call them whatever problems? It would be much easier.

**Posted:** Sun May 01, 2005 6:10 am

jensen

Harazi how did you post your message as stikies?can you tell me?Thanks a lot. Very Happy

**Posted:** Fri Aug 26, 2005 12:37 am

_________________
Our love is like the wind
... I can't see it ...
... But i can feel it ...

harazi

If only I knew... but I believe it is not my work, but rather the work of a superiour worker here... Wink

**Posted:** Fri Aug 26, 2005 12:42 am

Valentin Vornicu

**Posted:** Fri Aug 26, 2005 8:59 pm

_________________
We all use math everyday: to forecast weather, to tell time, to handle money; we also use math to analyze crime, reveal patterns, predict behavior. Using numbers we can solve the biggest mysteries we know.

Aryabhatta · Poincare Conjecture Offline Joined: 03 Apr 2005 Posts: 118

It seems like this site can do searches with latex input.

Maybe we (i.e. the forum program) can do a search for the formulas when some user tries to post a new topic. If we find matches, we don't let the user post, or if that is too harsh Mr. Green

, at least notify him/her that this problem might have been posted before and provide a link to the search results.

I checked some latex formula and it seems like the current search using latex formulas is not that good: there is too much noise. Maybe we can improve the search by having a latex formula specific search function, not sure how hard would that be to implement, but I think we could get a reasonable latex formula matcher implemented. If the matcher is smart enough, maybe it could even cope with renamed variables etc.

This matcher could then also be used to save the space used by the images too. I noticed that, even though we have the exact same looking formulas in different posts, the image files are different.

Just a thought.

**Posted:** Fri May 18, 2007 2:55 pm

Valentin Vornicu

These issues have been addressed many times. The problem is that it is hard to create such a program that will "recognize" $\LaTeX$ as users do. I have a working feature right now on the site, however it doesn't cover all the possible cases and outcomes. That is why (for now) it is harder to search in latex posts as well.

**Posted:** Fri May 18, 2007 3:26 pm

_________________
We all use math everyday: to forecast weather, to tell time, to handle money; we also use math to analyze crime, reveal patterns, predict behavior. Using numbers we can solve the biggest mysteries we know.