49. INTRODUCTION TO ANALYTIC GEOMETRY
... Analytic Geometry Analytic geometry, usually called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra ...
... Analytic Geometry Analytic geometry, usually called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra ...
Parallel and Perpendicular Lines
... If two lines are cut by a transversal such that corresponding angles are congruent, then the two lines are parallel. ...
... If two lines are cut by a transversal such that corresponding angles are congruent, then the two lines are parallel. ...
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... In this section we define the homology and cohomology groups associated to a simplicial complex K. We do so not because the homology of a simplicial complex is so intrinsically interesting in and of itself, but because the resulting homology theory is identical to the singular homology of the associ ...
... In this section we define the homology and cohomology groups associated to a simplicial complex K. We do so not because the homology of a simplicial complex is so intrinsically interesting in and of itself, but because the resulting homology theory is identical to the singular homology of the associ ...
Geometric Construction
... A triangle is a plane figure bounded by three straight lines and the sum of the interior angles is always 180o. ...
... A triangle is a plane figure bounded by three straight lines and the sum of the interior angles is always 180o. ...
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.