ترجمه مقاله نقش ضروری ارتباطات 6G با چشم انداز صنعت 4.0
- مبلغ: ۸۶,۰۰۰ تومان
ترجمه مقاله پایداری توسعه شهری، تعدیل ساختار صنعتی و کارایی کاربری زمین
- مبلغ: ۹۱,۰۰۰ تومان
Abstract
The theory of the isoptic curves is widely studied in the Euclidean plane E2 (see Cieślak et al., 1991 and Wieleitner, 1908 and the references given there). The analogous question was investigated by the authors in the hyperbolic H2 and elliptic E2 planes (see , and ), but in the higher dimensional spaces there are only few results in this topic. In Csima and Szirmai (2013) we gave a natural extension of the notion of the isoptic curves to the n -dimensional Euclidean space En(n≥3) which is called isoptic hypersurface. Now we develope an algorithm to determine the isoptic surface HP of a 3-dimensional polyhedron P. We will determine the isoptic surfaces for Platonic solids and for some semi-regular Archimedean polytopes and visualize them with Wolfram Mathematica ( Wolfram Research, Inc., 2015).