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July | 2010 | The Algorithmic Lens
https://cstheory.wordpress.com/2010/07
July 20, 2010. I spent this weekend working on and off a very interesting IMO problem – problem 6 from IMO 2006. You can find that here. It was a real hard nut and only led to a crushed ego😦. Let me first describe the problem and a result I managed to prove in this direction, which was however much weaker than the problem statement. IMO 2006 Problem 6 :. Assign to each side. Of a convex polygon. The maximum area of a triangle that has. As a side and is contained in. Is at least twice the area of. With a...
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Projections onto a Convex Body | The Algorithmic Lens
https://cstheory.wordpress.com/2010/08/23/projections-onto-a-convex-body
Projections onto a Convex Body. And an affine subspace. One can obviously define other notions of projection but the above is probably the most commonly used in geometry. If. Then the projected point. Is the unique point in. Such that the vector. Also is well known that projecting any segment to an affine subspace can only shrink its length. The proofs of these facts are easy to see. But in fact these facts are just corollaries of the following two results. Given any nonempty closed convex set. The entir...
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Jung’s Theorem | The Algorithmic Lens
https://cstheory.wordpress.com/2010/08/07/jungs-theorem
Given a set of points of diameter. It is trivial to see that it can be covered by a ball of radius. But the following theorem by Jung improves the result by a factor of about. And is the best possible. Theorem 1 [ Jung’s Theorem:. Be a set of points in. Then there is a ball of radius. Proof: We first prove this theorem for sets of points. And then extend it to an arbitrary point set. If. Then the smallest ball enclosing. Exists. We assume that its center is the origin. Denote its radius by. Then we have,.
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An IMO problem | The Algorithmic Lens
https://cstheory.wordpress.com/2010/07/20/an-imo-problem
I spent this weekend working on and off a very interesting IMO problem – problem 6 from IMO 2006. You can find that here. It was a real hard nut and only led to a crushed ego😦. Let me first describe the problem and a result I managed to prove in this direction, which was however much weaker than the problem statement. IMO 2006 Problem 6 :. Assign to each side. Of a convex polygon. The maximum area of a triangle that has. As a side and is contained in. Is at least twice the area of. Assign to each side.
cstheory.wordpress.com
The Algorithmic Lens | Page 2
https://cstheory.wordpress.com/page/2
July 10, 2008. In the last post I described a contravariant tensor of rank 1 and a covariant tensor of rank 1. In this post we will consider generalizations of these. We will introduce tensors of arbitrary rank. Is the number of contravariant indices and. Is the number of covariant indices. How many numbers does such a tensor represent? It is easy to see that if the tensor is defined in. Dimensional space, it defines. Therefore a tensor expression in which 1 index is to be summed upon expands into. Armed...
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Illinois tollways | The Algorithmic Lens
https://cstheory.wordpress.com/2010/02/23/illinois-tollways
So you missed paying toll – you did not have enough cash or you just zoomed in through the IPass lane. If that happened on the Golden Gate Bridge. You have a toll violation and you will end up paying a hefty fine. I remember back in 2008 I missed paying the toll because I was like 10c short and I had to pay 25$. No checks, credit cards, invitation cards, greeting cards or poker face appeals worked. That really sucked! You can follow any responses to this entry through the RSS 2.0. From your own site.
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Hello again! | The Algorithmic Lens
https://cstheory.wordpress.com/2010/02/06/hello-again
It has been one and a half years since I made a post. The last post was on the tensor Calculus. While I have still not dropped plans to complete the series at some point of time, I think it is simply unsustainable for me right now. I have pondered once in a while at the reason why I stopped blogging and here are some possible reasons. 2 I tend to plan quiet a lot before writing. This perfectionist attitude did not work well for me. You can follow any responses to this entry through the RSS 2.0. You are c...
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August | 2010 | The Algorithmic Lens
https://cstheory.wordpress.com/2010/08
Projections onto a Convex Body. August 23, 2010. And an affine subspace. One can obviously define other notions of projection but the above is probably the most commonly used in geometry. If. Then the projected point. Is the unique point in. Such that the vector. Also is well known that projecting any segment to an affine subspace can only shrink its length. The proofs of these facts are easy to see. But in fact these facts are just corollaries of the following two results. There is a unique point. To se...
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Some pointers for computer troublebombarding … | The Algorithmic Lens
https://cstheory.wordpress.com/2010/03/06/some-pointers-for-computer-troublebombarding
Some pointers for computer troublebombarding …. 1) QTParted – free software for resizing partitions (it can handle NTFS partitions) found in Knoppix Free CD. 2) Vista Recovery CD – available at http:/ neosmart.net/blog/2008/windows-vista-recovery-disc-download/. It is good to have these handy – keep a copy of the softwares on a CD and a printout of the document. They can save hours of your time (and lot of sanity) sometimes. You can follow any responses to this entry through the RSS 2.0. Next Post ».
