Ja n 19 95 Further Travels with My Ant
نویسنده
چکیده
A recurring theme of this column over the past four years has been what we have referred to as computer-generated mysteries. Examples are sequences defined by simple rational recursions whose terms turn out to be integers with interesting but unexplained divisibility properties, or geometric configurations that are observed to exist although there are no proofs of existence. In most of the examples the reported mysteries have remained unsolved and in some cases may in fact be, in a suitable sense, “unsolvable”. It is therefore gratifying to be able to present in this month’s column an elegant solution of a previously described mystery. An especially pleasing feature of this solution is the fact that the “breakthrough” was made possible by drawing the right picture. Once the picture is drawn it becomes clear what must be proved, after which further study of the pictures gives the clue as to how to construct the proof. It turns out that at one point one needs to use the Jordan curve theorem for a special class of closed curves. In the paragraphs to follow we shall present an informal but hopefully convincing argument which will require little more of the reader than the careful observation of a collection of pictures.
منابع مشابه
nt - p h / 99 01 06 8 v 1 2 6 Ja n 19 99 Could Grover ’ s quantum algorithm help in searching an actual database ?
I investigate whether it would technologically and economically make sense to build database search engines based on Grover's quantum search algorithm. The answer is not fully conclusive but in my judgement rather negative.
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A recurring theme of this column over the past four years has been what we have referred to as computer-generated mysteries. Examples are sequences de ned by simple rational recursions whose terms turn out to be integers with interesting but unexplained divisibility properties, or geometric con gurations that are observed to exist although there are no proofs of existence. In most of the exampl...
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