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differential geometry of surfaces

Wikipedia Summary

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within the surface as measured along curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied in depth by Carl Friedrich Gauss, who showed that curvature was an intrinsic property of a surface, independent of its isometric embedding in Euclidean space. Surfaces naturally arise as graphs of functions of a pair of variables, and sometimes appear in parametric form or as loci associated to space curves...
Related Codes (4)
Code
Description
Billable
Details
K02.6Dental caries on smooth surface
K02.61Dental caries on smooth surface limited to enamel
K02.62Dental caries on smooth surface penetrating into dentin
K02.63Dental caries on smooth surface penetrating into pulp

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