Surfaces | Differential topology
In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if "clockwise" is changed into "counterclockwise" after running through some loops in it, and coming back to the starting point. This means that a geometric shape, such as , that moves continuously along such a loop is changed into its own mirror image . A Möbius strip is an example of a non-orientable space. Various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms of differential forms. A generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space (a fiber bundle) for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values. (Wikipedia).
The idea of ‘atonement’ sounds very old-fashioned and is deeply rooted in religious tradition. To atone means, in essence, to acknowledge one’s capacity for wrongness and one’s readiness for apology and desire for change. It’s a concept that every society needs at its center. For gifts and
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👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
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CCSS What is an angle bisector
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
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Introduction to Angles (2 of 2: Definition & Basic Details)
More resources available at www.misterwootube.com
From playlist Angle Relationships
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👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
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Gradient (2 of 3: Angle of inclination)
More resources available at www.misterwootube.com
From playlist Further Linear Relationships
CCSS What is the difference between Acute, Obtuse, Right and Straight Angles
👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
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2D Equilibrium -- Balancing Games
How does everything even out? Learn what 2D Equilibrium is and how it effects the balance of life. License: Creative Commons BY-NC-SA More information at http://k12videos.mit.edu/terms-conditions
From playlist Measurement
Determining if two angles are adjacent or not
👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships
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In this lecture, we continue our discussion of cross products of planar vectors and move towards a famous and useful formula of J. Meister. This is a lecture in the Algebraic Calculus One course, which will present an exciting new approach to calculus, sticking with rational numbers and
From playlist Algebraic Calculus One from Wild Egg
Robert YOUNG - Quantifying nonorientability and filling multiples of embedded curves
Abstract: https://indico.math.cnrs.fr/event/2432/material/17/0.pdf
From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
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From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
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In this video we introduce polygonal splines, through a preliminary discussion of data structures. Then we extend our notion of signed areas from polygons to polygonal splines. Along the way we introduce cyclic oriented data structures, together with a special notation for cyclic lists a
From playlist Algebraic Calculus One from Wild Egg
Topological Analysis of Grain Boundaries - Srikanth Patala
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From playlist Mathematics
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This is the fourth of four lectures from Dominic Joyce's 3rd Year Geometry of Surfaces course. The four lectures cover topological surfaces and conclude with a big result, namely the classification of surfaces. This lecture covers connected sums, orientations, and finally the classificatio
From playlist Oxford Mathematics Student Lectures - Geometry of Surfaces
Quantifying nonorientability and filling multiples of embedded curves - Robert Young
Analysis Seminar Topic: Quantifying nonorientability and filling multiples of embedded curves Speaker: Robert Young Affiliation: New York University; von Neumann Fellow, School of Mathematics Date: October 5, 2020 For more video please visit http://video.ias.edu
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Orientations of Graphs | Directed Graphs, Digraph Theory
What is an orientation of a graph? We'll be going over the definition of this directed graph concept and some examples in today's lesson! Support Wrath of Math on PayPal: paypal.me/wrathofmath Given an undirected graph G, an orientation of G is a directed graph obtained by assigning a di
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Non-Orientable Knot Genus and the Jones Polynomial - Efstratia Kalfagianni
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👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a
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