Don't Intersect Please :D

For students of class 6-8 (age 12 to 14)
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Thamim Zahin
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Don't Intersect Please :D

Unread post by Thamim Zahin » Tue Feb 28, 2017 7:19 pm

Given $2n$ points in the plane with no three collinear, show that it is possible to pair them up in such a way that the $n$ line segments joining paired points do not intersect.
I think we judge talent wrong. What do we see as talent? I think I have made the same mistake myself. We judge talent by the trophies on their showcases, the flamboyance the supremacy. We don't see things like determination, courage, discipline, temperament.

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ahmedittihad
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Re: Don't Intersect Please :D

Unread post by ahmedittihad » Sun Mar 05, 2017 4:43 pm

Take the convex hull and select two consecutive points and pair them up. Then take the next convex hull and do the algorithm. We eventually will get what we desire.
Frankly, my dear, I don't give a damn.

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Thamim Zahin
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Re: Don't Intersect Please :D

Unread post by Thamim Zahin » Sun Mar 05, 2017 6:42 pm

Simple polygon will also do the trick. Isn't? If we put a super big rubber-band, it will result us a simple polygon.
I think we judge talent wrong. What do we see as talent? I think I have made the same mistake myself. We judge talent by the trophies on their showcases, the flamboyance the supremacy. We don't see things like determination, courage, discipline, temperament.

Absur Khan Siam
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Location: Bashaboo , Dhaka

Re: Don't Intersect Please :D

Unread post by Absur Khan Siam » Sun Mar 05, 2017 10:41 pm

Actually,@thamimzahin,the idea which you have is the main concept of convex hull.
http://mathworld.wolfram.com/ConvexHull.html
Last edited by Absur Khan Siam on Mon Mar 06, 2017 4:46 pm, edited 1 time in total.

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ahmedittihad
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Re: Don't Intersect Please :D

Unread post by ahmedittihad » Sun Mar 05, 2017 11:41 pm

@thamimzahin I seem to remember to have taught you the concept of a convex hull. Did you forget already? :lol:
Frankly, my dear, I don't give a damn.

Absur Khan Siam
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Location: Bashaboo , Dhaka

Re: Don't Intersect Please :D

Unread post by Absur Khan Siam » Mon Mar 06, 2017 12:03 pm

I think 70% or more are introduced to convex hull by this 'rubber-band' concept.:D

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ahmedittihad
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Re: Don't Intersect Please :D

Unread post by ahmedittihad » Mon Mar 06, 2017 4:11 pm

Related Problem,
Given $2n$ points in a plane with no three collinear, with $n$ red points and $n$ blue points, prove that
there exists a pairing of the red and blue points such that the $n$ segments joining each pair are pairwise
non-intersecting.
Frankly, my dear, I don't give a damn.

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Thanic Nur Samin
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Re: Don't Intersect Please :D

Unread post by Thanic Nur Samin » Mon Mar 06, 2017 6:13 pm

Thamim Zahin wrote:Given $2n$ points in the plane with no three collinear, show that it is possible to pair them up in such a way that the $n$ line segments joining paired points do not intersect.
Here is my take.

Take all possible pairings of the points, and select the one with minimum sum of the length of the segments. Due to the triangle inequality, the segments do not intersect.

The argument works in Ittihad's problem as well.
Hammer with tact.

Because destroying everything mindlessly isn't cool enough.

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