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Net (polyhedron) A net of a regular dodecahedron. The eleven nets of a cube. In geometry, a net of a polyhedron is an arrangement of non-overlapping edge -joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general ...
Moving sofa problem. What is the largest area of a shape that can be maneuvered through a unit-width L-shaped corridor? In mathematics, the moving sofa problem or sofa problem is a two-dimensional idealization of real-life furniture-moving problems and asks for the rigid two-dimensional shape of the largest area that can be maneuvered through ...
Erdős distinct distances problem. In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 [1][2] and almost proven by Larry Guth and Nets Katz in 2015. [3][4][5]
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The truncated icosahedron is an Archimedean solid, meaning it is a highly symmetric and semi-regular polyhedron, and two or more different regular polygonal faces meet in a vertex. [5] It has the same symmetry as the regular icosahedron, the icosahedral symmetry, and it also has the property of vertex-transitivity. [6][7] The polygonal faces ...
The Erdős Distance Problem is a monograph on the Erdős distinct distances problem in discrete geometry: how can one place points into -dimensional Euclidean space so that the pairs of points make the smallest possible distance set? It was written by Julia Garibaldi, Alex Iosevich, and Steven Senger, and published in 2011 by the American ...