Shallow Sections of the Hypercube
نویسندگان
چکیده
Consider a d-dimensional closed ball B whose center coincides with that of the hypercube [0, 1]d. Pick radius in such way vertices are outside and midpoints its edges interior B. It is known that, when d ≥ 3, (d − 1)-dimensional volume H∩[0, 1]d, where H hyperplane ℝd tangent to B, largest possible if only orthogonal diagonal hypercube. shown here same holds 5 but required contain centers square faces
منابع مشابه
Slices, Slabs, and Sections of the Unit Hypercube
Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a flat defined by two parallel hyperplanes. We also describe some of the history of these problems, dating to Pólya’s Ph.D. thesis, and we discuss several applications of these formulas.
متن کاملthe relationship between learners critical thinking ability and their performance in the reading sections of the tofel and ielts test
the study reflected in this thesis aims at finding out relationships between critical thinking (ct), and the reading sections of tofel and ielts tests. the study tries to find any relationships between the ct ability of students and their performance on reading tests of tofel and academic ielts. however, no research has ever been conducted to investigate the relationship between ct and the read...
15 صفحه اولa comparative move analysis of the introduction sections of ma theses by iranian and native post-graduate students
since esp received universal attention to smooth the path for academic studies and productions, a great deal of research and studies have been directed towards this area. swales’ (1990) model of ra introduction move analysis has served a pioneering role of guiding many relevant studies and has proven to be productive in terms of helpful guidelines that are the outcome of voluminous productions ...
15 صفحه اولA shallow-water theory for annular sections of Keplerian Disks
Context. A scaling argument is presented that leads to a shallow water theory of non-axisymmetric disturbances in annular sections of thin Keplerian disks. Aims. To develop a theoretical construction that will aid in physically understanding the relationship of known twodimensional vortex dynamics to their three-dimensional counterparts in Keplerian disks. Methods. Using asymptotic scaling argu...
متن کاملthe effect of taftan pozzolan on the compressive strength of concrete in the environmental conditions of oman sea (chabahar port)
cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...
ذخیره 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: Israel Journal of Mathematics
سال: 2022
ISSN: ['1565-8511', '0021-2172']
DOI: https://doi.org/10.1007/s11856-022-2400-9