![Lines: What are they good for anyway?](http://s1.studyres.com/store/data/008400569_1-72f07a9aa7276d2b717c46f4b168ef36-300x300.png)
3.5 Using Properties of Parallel Lines
... Standard 3: Students will learn and apply geometric concepts. Objectives: Use properties of parallel lines in real-life situations, such as building a CD rack. Construct parallel lines using a straight edge and a compass. To understand how light bends when it passes through glass or water. ...
... Standard 3: Students will learn and apply geometric concepts. Objectives: Use properties of parallel lines in real-life situations, such as building a CD rack. Construct parallel lines using a straight edge and a compass. To understand how light bends when it passes through glass or water. ...
Statements equivalent to Euclid`s Parallel (5th) Postulate
... Statements equivalent to Euclid's Parallel (5th) Postulate In Neutral Geometry (Euclid's Postulates 1 - 4 clarified and made precise) the following statements are equivalent: • (Euclid's 5th) If two lines are intersected by a transversal in such a way that the sum of the two interior angles on one s ...
... Statements equivalent to Euclid's Parallel (5th) Postulate In Neutral Geometry (Euclid's Postulates 1 - 4 clarified and made precise) the following statements are equivalent: • (Euclid's 5th) If two lines are intersected by a transversal in such a way that the sum of the two interior angles on one s ...
Riemannian connection on a surface
![](https://commons.wikimedia.org/wiki/Special:FilePath/Levi-Civita_1930.jpeg?width=300)
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.