Isometry

:For the mechanical engineering and architecture usage, see isometric projection.

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In mathematics, an isometry, isometric isomorphism or congruence mapping is a distance-preserving isomorphism between metric spaces. Geometric figures which can be related by an isometry are called congruent.

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Isometries are often used in constructions where one space is embedded in another space. For instance, the completion of a metric space M involves an isometry from M into M', a quotient set of the space of Cauchy sequences on M. The original space M is thus isometrically isomorphic to a subspace of a complete metric space, and it is usually identified with this subspace. Other embedding constructions show that every metric space is isometrically isomorphic to a closed subset of some normed vector space and that every complete metric space is isometrically isomorphic to a closed subset of some Banach space.

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Mechanical engineering: Mechanical engineering is the application of physical principles to the creation of useful reality for machine design. Such solid models may be used as the basis for finite element analysis (FEA) and / or computational fluid dynamics (CFD) of the design. Through the application of computer-aided man...

Architecture: Architecture (in Greek αρχή = first and τέχνη = craftsmanship) is the art and science of designing buildings and structures. A wider definition would include within its scope the design of the total built environment, from the macrolevel of town planning,...

Isometric projection: Isometric projection is a form of orthographic projection, or more specifically, an axonometric projection. It is a method for the visual representation of three-dimensional objects in two dimensions in which the angles between the projection of the x, y, and z axes are all the same, or 120°. F...