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Double Bubble Conjecture
In the mathematical theory of minimal surfaces, the double bubble theorem states that the shape that encloses and separates two given volumes and has the minimum possible surface area is a ''standard double bubble'': three spherical surfaces meeting at angles of 120° on a common circle. The double bubble theorem was formulated and thought to be true in the 19th century, and became a "serious focus of research" by 1989, but was not proven until 2002. The proof combines multiple ingredients. Compactness of rectifiable currents (a generalized definition of surfaces) shows that a solution exists. A symmetry argument proves that the solution must be a surface of revolution, and it can be further restricted to having a bounded number of smooth pieces. Jean Taylor proof of Plateau's laws describes how these pieces must be shaped and connected to each other, and a final case analysis shows that, among surfaces of revolution connected in this way, only the standard double bubble has loc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Planar Double Bubbles
Planar is an adjective meaning "relating to a plane (geometry)". Planar may also refer to: Science and technology * Planar (computer graphics), computer graphics pixel information from several bitplanes * Planar (transmission line technologies), transmission lines with flat conductors * Planar, the structure resulting from the planar process used in the manufacture of semiconductor devices, such as planar transistors * Planar graph, graph that can be drawn in the plane so that no edges cross * Planar mechanism, a system of parts whose motion is constrained to a two-dimensional plane * Planar Systems, an Oregon-headquartered manufacturer of digital displays * Zeiss Planar, photographic lens designed by Paul Rudolph at Carl Zeiss in 1896 See also * List of planar symmetry groups * Planarity, a computer puzzle game * Plane (other) * Planer (other) * {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
