Volume of convex polytopes equals mixed volume of simplices
نویسندگان
چکیده
qaaa We provide a simple proof for the equality between normalized volume of convex polytope with m vertices and mixed simplices thus show seemingly restrictive problem computing is still at least as hard volumes polytopes in general.
منابع مشابه
Approximation of convex bodies by inscribed simplices of maximum volume
The Banach-Mazur distance between an arbitrary convex body and a simplex in Euclidean n-space En is at most n+2. We obtain this estimate as an immediate consequence of our theorem which says that for an arbitrary convex body C in En and for any simplex S of maximum volume contained in C the homothetical copy of S with ratio n + 2 and center in the barycenter of S contains C . In general, this r...
متن کاملVolume form as volume of infinitesimal simplices
In the context of Synthetic Differential Geometry, we describe the square volume of a “second-infinitesimal simplex”, in terms of square-distance between its vertices. The square-volume function thus described is symmetric in the vertices. The square-volume gives rise to a characterization of the volume form in the top dimension.
متن کاملMonochromatic simplices of any volume
We give a very short proof of the following result of Graham from 1980: For any finite coloring of R, d ≥ 2, and for any α > 0, there is a monochromatic (d + 1)tuple that spans a simplex of volume α. Our proof also yields new estimates on the number A = A(r) defined as the minimum positive value A such that, in any rcoloring of the grid points Z of the plane, there is a monochromatic triangle o...
متن کاملthe pathology of historical texts translation: a study of persian translations of 7th volume of cambridge history of iran
ترجمه با گسترش زبان آغاز شده و اهمیت آن روز به روز افزایش می یابد، و برای اولین بار به عنوان شاخه ای از دانش و روشی برای انتقال علوم، فرهنگ و تجربه در در دوره قاجار در ایران آغاز شد. در حقیقت متون تاریخی از اولین متونی هستند که در ایران ترجمه شدند چرا که به سیاستمداران آن دوره کمک می کردند تا به علل موفقیت جهان غرب و پیشرفت هایشان در طول تاریخ پی ببرند، بنابراین به تدریج ترجمه این گونه متون رون...
15 صفحه اولVolume and Lattice Points of Reflexive Simplices
Using new number-theoretic bounds on the denominators of unit fractions summing up to one, we show that in any dimension d ≥ 4 there is only one d-dimensional reflexive simplex having maximal volume. Moreover, only these reflexive simplices can admit an edge that has the maximal number of lattice points possible for an edge of a reflexive simplex. In general, these simplices are also expected t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2023
ISSN: ['0003-889X', '1420-8938']
DOI: https://doi.org/10.1007/s00013-023-01836-3