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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 Clay Institute was inspired by a set of twenty-three problems organized by the mathematician David Hilbert in 1900 which were highly influential in driving the progress of mathematics in the twentieth century. [1] The seven selected problems span a number of mathematical fields, namely algebraic geometry, arithmetic geometry, geometric ...
Pages in category "Unsolved problems in geometry" The following 48 pages are in this category, out of 48 total. This list may not reflect recent changes. A.
Many of these problems are easily solvable provided that other geometric transformations are allowed; for example, neusis construction can be used to solve the former two problems. In terms of algebra , a length is constructible if and only if it represents a constructible number , and an angle is constructible if and only if its cosine is a ...
The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A/2 and r = 1. The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ, is the area of a spherical cap on a unit sphere
From 32, 31 must be subtracted and attributed to the Veronese, to leave the correct answer (from the point of view of geometry), namely 1. This process of attributing intersections to 'degenerate' cases is a typical geometric introduction of a 'fudge factor'.