منابع مشابه
Regular Simplices Passing through Holes
What is the smallest circular or square wall hole that a regular tetrahedron can pass? This problem was solved by Itoh–Tanoue– Zamfirescu [8]. Then, we settled the case of equilateral triangular hole in [1]. Motivated by these results, we consider the corresponding problems in higher dimensions. Among other results, we determine the minimum (n−1)-dimensional ball hole that a unit regular n-simp...
متن کاملConvex bodies passing through holes
For a given convex body, find a “small” wall hole through which the convex body can pass. This type of problems goes back to Zindler [14] in 1920, who considered a convex polytope which can pass through a fairly small circular holes. A related topic known as Prince Rupert’s problem can be found in [2]. Here we concentrate on the case when the convex body is a regular tetrahedron or a regular n-...
متن کاملA Statistical Characterization of Regular Simplices
Picture three points at the vertices of an equilateral triangle in two dimensions, or four points at the vertices of a regular tetrahedron in three dimensions. Thought of as scatterings of data they wouldn’t seem to reveal strong linear associations between the coordinates. There are no clear axes of elongation in the scatterplots, which would suggest that change in some variable is predictable...
متن کاملLarge regular simplices contained in a hypercube
We prove that the n-dimensional unit hypercube contains an n-dimensional regular simplex of edge length c √ n, where c > 0 is a constant independent of n. Let l∆n be the n-dimensional regular simplex of edge length l, and let lQn be the n-dimensional hypercube of edge length l. For simplicity, we omit l if l= 1, e.g., Qn denotes the unit hypercube. We are interested in the maximum edge length o...
متن کاملRegular Black Holes and Confinement
Properties of the rotating Kerr-Newman black hole solution allow to relate it with spinning particles. Singularity of black hole (BH) can be regularized by a metric deformation. In this case, as a consequence of the Einstein equations, a material source appears in the form of relativistically rotating superconducting disk which replaces the former singular region. We show a relation of the BH r...
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: Geometriae Dedicata
سال: 2009
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-009-9399-5