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5 days ago · Platonic solid. In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
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- Convex Polytope
A 3-dimensional convex polytope. A convex polytope is a...
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5 days ago · 3D model of a regular tetrahedron. In geometry, a tetrahedron ( pl.: tetrahedra or tetrahedrons ), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. The tetrahedron is the simplest of all the ordinary convex polyhedra.
- F = 4, E = 6V = 4 (χ = 2)
- {3,3}
- 4 {3}
- Platonic solid
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3 days ago · This concise, self-contained volume introduces convex analysis and optimization algorithms, with an emphasis on bridging the two areas. It explores cutting-edge algorithms-such as the proximal gradient, Douglas-Rachford, Peaceman-Rachford, and FISTA-that have applications in machine learning, signal processing, image reconstruction, and other ...
1 day ago · Use of Newton's method to compute square roots. Newton's method is one of many known methods of computing square roots. Given a positive number a, the problem of finding a number x such that x2 = a is equivalent to finding a root of the function f(x) = x2 − a. The Newton iteration defined by this function is given by.
4 days ago · Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. [a] The graph of a quadratic function (with ) is a parabola with its axis parallel to the y -axis.
4 days ago · The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The integral is evaluated for all values of shift, producing the convolution function.
1 day ago · Archimedes computed upper and lower bounds of π by drawing a regular hexagon inside and outside a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating the perimeters of these polygons, he proved that 223 / 71 < π < 22 / 7 (that is, 3.1408 < π < 3.1429).
