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A diagram in the notation consists of several shapes linked together by lines. The notation widely appears in modern quantum theory , particularly in matrix product states and quantum circuits . In particular, categorical quantum mechanics (which includes ZX-calculus ) is a fully comprehensive reformulation of quantum theory in terms of Penrose ...
The divergence at a point represents the degree to which a small volume around the point is a source or a sink for the vector flow, a result which is made precise by the divergence theorem. The divergence can also be defined on a Riemannian manifold , that is, a manifold with a Riemannian metric that measures the length of vectors.
The Borromean rings have been used in different contexts to indicate strength in unity. [14] In particular, some have used the design to symbolize the Trinity. [3] A 13th-century French manuscript depicting the Borromean rings labeled as unity in trinity was lost in a fire in the 1940s, but reproduced in an 1843 book by Adolphe Napoléon Didron.
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 ...
In other words, the circle is the locus of points that represent the state of stress on individual planes at all their orientations, where the axes represent the principal axes of the stress element. 19th-century German engineer Karl Culmann was the first to conceive a graphical representation for stresses while considering longitudinal and ...
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
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In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.