It is conjectured that the Mandelbrot set is locally connected. This famous conjecture is known as MLC (for Mandelbrot Locally Connected). By the work of Adrien Douady and John H. Hubbard, this conjec ...
Margulis was born in Moscow, Soviet Union. He received his PhD in 1970 from the Moscow State University, starting research in ergodic theory under the supervision of Yakov Sinai. Early work with David ...
The term "ergodic" was derived from the Greek words ?ργον (ergon: "work") and οδ?? (odos: "path" or "way"). It was chosen by Boltzmann while he was working on a problem in statistical mechani ...
Hillel Furstenberg was born in Germany, in 1935, and the family emigrated to the United States in 1939, shortly before the outbreak of the Second World War. He attended Marsha Stern Talmudical Academy ...
The concept of a dynamical system has its origins in Newtonian mechanics. There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is an implicit relati ...
Many different nets can exist for a given polyhedron, depending on the choices of which edges are joined and which are separated. Conversely, a given net may fold into more than one different convex p ...
Many examples of bounded convex polytopes can be found in the article "polyhedron".In the 2-dimensional case the full-dimensional examples are a half-plane, a strip between two parallel lines, an angl ...
Many different nets can exist for a given polyhedron, depending on the choices of which edges are joined and which are separated. Conversely, a given net may fold into more than one different convex p ...
The moving sofa problem was formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem is a two-dimensional idealisation of real-life furniture moving problems, and asks for the ...
For example, a circular disk of radius 1/2 can accommodate any plane curve of length 1 by placing the midpoint of the curve at the center of the disk. Another possible solution has the shape of a rhom ...
Let C be a Jordan curve. A polygon P is inscribed in C if all vertices of P belong to C. The inscribed square problem asks:Does every Jordan curve admit an inscribed square?It is not required that the ...
Consider a periodic tiling by unit squares (it looks like infinite graph paper). Now cut one square into two rectangles. The tiling obtained in this way is non-periodic: there is no non-zero shift tha ...
In the mathematical theory of tessellations, a prototile is one of the shapes of a tile in a tessellation.A tessellation of the plane or of any other space is a cover of the space by closed shapes, ca ...
The Elements are mainly a systematization of earlier knowledge of geometry. Its superiority over earlier treatments was rapidly recognized, with the result that there was little interest in preserving ...
In discrete and computational geometry, a set of points in the Euclidean plane is said to be in convex position or convex independent if none of the points can be represented as a convex combination o ...
