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Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.
In classical mechanics, a branch overlapping in physics and applied mathematics, mechanical similarity occurs when the potential energy is a homogeneous function of the positions of the particles, with the result that the trajectories of the particles in the system are geometrically similar paths, differing in size but retaining shape.
Table of Shapes Section Sub-Section Sup-Section Name Algebraic Curves ¿ Curves ¿ Curves: Cubic Plane Curve: Quartic Plane Curve: Rational Curves: Degree 2: Conic Section(s) Unit Circle: Unit Hyperbola: Degree 3: Folium of Descartes: Cissoid of Diocles: Conchoid of de Sluze: Right Strophoid: Semicubical Parabola: Serpentine Curve: Trident ...
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines , are statistically self-similar: parts of them show the same statistical properties at many scales. [ 2 ]
Symmetry in physics has been generalized to mean invariance—that is, lack of change—under any kind of transformation, for example arbitrary coordinate transformations. [17] This concept has become one of the most powerful tools of theoretical physics , as it has become evident that practically all laws of nature originate in symmetries.
Supreme Court Chief Justice John Roberts slammed what he described as “dangerous” talk by some officials about ignoring federal court rulings, using an annual report weeks before President ...
The College Football Playoff cake is getting close to baked, which means much of the angst and anger of the past few weeks over hypothetical and projected scenarios have proved a waste of time.
These transformations produce similar shapes, which is the basis of trigonometry. In contrast, angles and ratios are not invariant under non-uniform scaling (such as stretching). The sum of a triangle's interior angles (180°) is invariant under all the above operations.
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