Squaring the circle: academic and entertaining
نویسندگان
چکیده
منابع مشابه
Borel circle squaring
We give a completely constructive solution to Tarski’s circle squaring problem. More generally, we prove a Borel version of an equidecomposition theorem due to Laczkovich. If k ≥ 1 and A,B ⊆ Rk are bounded Borel sets with the same positive Lebesgue measure whose boundaries have upper Minkowski dimension less than k, then A and B are equidecomposable by translations using Borel pieces. This answ...
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Laczkovich proved that if bounded subsets A and B of R have the same non-zero Lebesgue measure and the upper box dimension of the boundary of each set is less than k, then there is a partition of A into finitely many parts that can be translated to form a partition of B. Here we show that it can be additionally required that each part is both Baire and Lebesgue measurable. As special cases, thi...
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Innovation and entrepreneurship are prominent buzz words in the modern lexicon, reflective of the knowledge economy in which we now dwell. While the possibilities in a world of big data, robotics, and the internet of everything seem endless, they do indeed have limits. Cities, it has become routine to point out, are the harbingers of innovation, and attract creative people who develop and apply...
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ژورنال
عنوان ژورنال: English Today
سال: 2005
ISSN: 0266-0784,1474-0567
DOI: 10.1017/s0266078405002014