Book Review: Geometry of sets and measures in Euclidean spaces
نویسندگان
چکیده
منابع مشابه
Spatial Analysis in curved spaces with Non-Euclidean Geometry
The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...
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A finite set H in Rd is called an acute set if any angle determined by three points of H is acute. We examine the maximal cardinality α(d) of a d-dimensional acute set. The exact value of α(d) is known only for d ≤ 3. For each d ≥ 4 we improve on the best known lower bound for α(d). We present different approaches. On one hand, we give a probabilistic proof that α(d) > c · 1.2d. (This improves ...
متن کاملUltrametric sets in Euclidean point spaces
Finite sets S of points in a Euclidean space the mutual distances of which satisfy the ultrametric inequality (A;B) maxf (A;C); (C;B)g for all points in S are investigated and geometrically characterized. Inspired by results on ultrametric matrices and previous results on simplices, connections with so-called centered metric trees as well as with strongly isosceles right simplices are found. AM...
متن کاملBook Review: János Bolyai, Non-Euclidean Geometry, and the Nature of Space, Volume 52, Number 9
This attractive little volume consists of two major components, together with a number of shorter sections. The major components are labeled " Introduction " and " Appendix " respectively , both designations grossly understating their content. The " Appendix " consists of Bolyai's revolutionary tract, with the subtitle " THE SCIENCE ABSOLUTE OF SPACE Independent of the Truth or Falsity of Eucli...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1997
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-97-00725-8