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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 ...
Packing of irregular objects is a problem not lending itself well to closed form solutions; however, the applicability to practical environmental science is quite important. For example, irregularly shaped soil particles pack differently as the sizes and shapes vary, leading to important outcomes for plant species to adapt root formations and ...
An arrangement in which the midpoint of all the spheres lie on a single straight line is called a sausage packing, as the convex hull has a sausage-like shape.An approximate example in real life is the packing of tennis balls in a tube, though the ends must be rounded for the tube to coincide with the actual convex hull.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
The complete list remains an open problem. [29] If one relaxes the requirement that the tetrahedra be all the same shape, one can tile space using only tetrahedra in many different ways. For example, one can divide an octahedron into four identical tetrahedra and combine them again with two regular ones.
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 an L-shaped planar region with legs of unit width. [1] The area thus obtained is referred to as the sofa constant.
A college student just solved a seemingly paradoxical math problem—and the answer came from an incredibly unlikely place. Skip to main content. 24/7 Help. For premium support please call: 800 ...
Convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis and discrete mathematics. [131] It has close connections to convex analysis , optimization and functional analysis and important applications in number theory .