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08. Non-Euclidean Geometry 1. Euclidean Geometry
08. Non-Euclidean Geometry 1. Euclidean Geometry

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... -Explain that if a tangent and a secant intersect at a point of tangency that the angle formed is half of the intercepted arc. -Explain that the angle formed by 2 secants outside a circle is half of the difference of the intercepted arcs. -Explain that the angle formed by 2 secants inside a circle i ...
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< 1 ... 59 60 61 62 63 64 65 66 67 ... 81 >

Riemannian connection on a surface



For the classical approach to the geometry of surfaces, see Differential geometry of surfaces.In mathematics, the Riemannian connection on a surface or Riemannian 2-manifold refers to several intrinsic geometric structures discovered by Tullio Levi-Civita, Élie Cartan and Hermann Weyl in the early part of the twentieth century: parallel transport, covariant derivative and connection form . These concepts were put in their final form using the language of principal bundles only in the 1950s. The classical nineteenth century approach to the differential geometry of surfaces, due in large part to Carl Friedrich Gauss, has been reworked in this modern framework, which provides the natural setting for the classical theory of the moving frame as well as the Riemannian geometry of higher-dimensional Riemannian manifolds. This account is intended as an introduction to the theory of connections.
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