Intrinsic Metrics on Sierpinski-Like Triangles and Their Geometric Properties
نویسندگان
چکیده
منابع مشابه
Basic Geometric Properties of Triangles
In this work, we define angles between vectors and between three points. Building on this, we prove basic geometric properties of triangles, such as the Isosceles Triangle Theorem, the Law of Sines and the Law of Cosines, that the sum of the angles of a triangle is π, and the congruence theorems for triangles. The definitions and proofs were developed following those by John Harrison in HOL Lig...
متن کاملOn C3-Like Finsler Metrics
In this paper, we study the class of of C3-like Finsler metrics which contains the class of semi-C-reducible Finsler metric. We find a condition on C3-like metrics under which the notions of Landsberg curvature and mean Landsberg curvature are equivalent.
متن کاملAlgorithmic Self-Assembly of DNA Sierpinski Triangles
Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern--a Si...
متن کاملStrict Self-assembly of Discrete Sierpinski Triangles
Winfree (1998) showed that discrete Sierpinski triangles can self-assemble in the Tile Assembly Model. A striking molecular realization of this self-assembly, using DNA tiles a few nanometers long and verifying the results by atomic-force microscopy, was achieved by Rothemund, Papadakis, and Winfree (2004). Precisely speaking, the above self-assemblies tile completely filled-in, two-dimensional...
متن کاملGeometric Modelling of a Class of Sierpinski-type Fractals and Their Geometric Constructions
Study on properties of Sierpinski-type fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. It is well know that studying fractal theory relies on in-depth observation and analysis to topological structures of fractals and their geometric constructions. But most works of simulating fractals are for graphical goal and often done by non-mathematical researchers....
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: Symmetry
سال: 2018
ISSN: 2073-8994
DOI: 10.3390/sym10060204