Differential geometry | Differential topology

Tangent space

In mathematics, the tangent space of a manifold generalizes to higher dimensions the notion of tangent planes to surfaces in three dimensions and tangent lines to curves in two dimensions. In the context of physics the tangent space to a manifold at a point can be viewed as the space of possible velocities for a particle moving on the manifold. (Wikipedia).

Tangent space
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How to determine the value of x using the definition of a tangent line to a circle

Learn how to solve problems with tangent line. A tangent line to a circle is a line that touches the circle at exactly one point. The tangent line to a circle makes a right angle with the radius of the circle at the point of its tangency. Thus, to solve for any missing value involving the

From playlist Circles

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Equations of Tangents & Normals

More resources available at www.misterwootube.com

From playlist Applications of Differentiation

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What is a tangent plane

The "tangent plane" of the graph of a function is, well, a two-dimensional plane that is tangent to this graph. Here you can see what that looks like.

From playlist Multivariable calculus

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Manifolds #5: Tangent Space (part 1)

Today, we introduce the notion of tangent vectors and the tangent vector space at a point on a manifold.

From playlist Manifolds

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Geometry - Basic Terminology (26 of 34) What are Tangent Lines?

Visit http://ilectureonline.com for more math and science lectures! In this video I will define the tangent line in relation to the circle. Next video in the Basic Terminology series can be seen at: http://youtu.be/CvEL2McGX0M

From playlist GEOMETRY 1 - BASIC TERMINOLOGY

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Find the point where their exist a horizontal tangent line

πŸ‘‰ Learn how to find the point of the horizontal tangent of a curve. A tangent to a curve is a line that touches a point in the outline of the curve. When given a curve described by the function y = f(x). The value of x for which the derivative of the function y, is zero is the point of hor

From playlist Find the Point Where the Tangent Line is Horizontal

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Manifolds 4.1 : Introduction to the Tangent Space

In this video, I introduce the tangent space, and prove that the tangent space of arbitrary euclidean space is the same dimensional (real) vector space. Translate This Video : Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://teespring.com/stores/femat

From playlist Manifolds

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Tangent Tangent Angle Theorems - Circles & Arc Measures - Geometry

This geometry video tutorial provides a basic introduction into tangent tangent angle theorems as it relates to circles and arc measures. The sum of the minor arc and the tangent tangent angle is supplementary. The two angles add up to 180. This tutorial contains plenty of examples and

From playlist Geometry Video Playlist

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Find the values where the function has horizontal tangents

πŸ‘‰ Learn how to find the point of the horizontal tangent of a curve. A tangent to a curve is a line that touches a point in the outline of the curve. When given a curve described by the function y = f(x). The value of x for which the derivative of the function y, is zero is the point of hor

From playlist Find the Point Where the Tangent Line is Horizontal

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What is a Tensor 15: Coordinate Transformations

What is a Tensor 15: Coordinate Transformations

From playlist What is a Tensor?

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OpenGL - normal maps

Code samples derived from work by Joey de Vries, @joeydevries, author of https://learnopengl.com/ All code samples, unless explicitly stated otherwise, are licensed under the terms of the CC BY-NC 4.0 license as published by Creative Commons, either version 4 of the License, or (at your o

From playlist OpenGL

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Hyperbolic Graph Convolutional Networks | Geometric ML Paper Explained

❀️ Become The AI Epiphany Patreon ❀️ https://www.patreon.com/theaiepiphany πŸ‘¨β€πŸ‘©β€πŸ‘§β€πŸ‘¦ Join our Discord community πŸ‘¨β€πŸ‘©β€πŸ‘§β€πŸ‘¦ https://discord.gg/peBrCpheKE In this video we dig deep into the hyperbolic graph convolutional networks paper introducing a class of GCNs operating in the hyperbolic spa

From playlist Graph Neural Nets

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What is a Manifold? Lesson 13: The tangent bundle - an illustration.

What is a Manifold? Lesson 13: The tangent bundle - an illustration. Here we have a close look at a complete example using the tangent bundle of the manifold S_1. Next lesson we look at the Mobius strip as a fiber bundle.

From playlist What is a Manifold?

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What is General Relativity? Lesson 18: The Geodesic Equation Part 1

Lesson 18: The Geodesic Equation Part 1 We derive the geodesic equation from a mathematical point of view beginning with a manifold, a curve, a connection, and a parameterization of the curve. Check out the forums at http://xylyxylyx.freeforums.net/ and the Patreon page at https://www.

From playlist What is General Relativity?

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What is a Manifold? Lesson 11: The Cotangent Space

What is a Manifold? Lesson 11: The Cotangent Space I have annotated an obvious error at 2:00. However annotations are not visible on mobile devices!

From playlist What is a Manifold?

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Differential Forms | Introduction and the Tangent Space

The is the first of a series of videos devoted to differential forms, building up to a generalized version of Stoke's Theorem. Here we look at the notion of a tangent space to a curve at a point and the tangent space of R^2. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_c

From playlist Differential Forms

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Using the idea that two tangent lines from a point are equal find the perimeter of a circle

Learn how to solve problems with tangent line. A tangent line to a circle is a line that touches the circle at exactly one point. The tangent line to a circle makes a right angle with the radius of the circle at the point of its tangency. Thus, to solve for any missing value involving the

From playlist Circles

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CS224W: Machine Learning with Graphs | 2021 | Lecture 19.2 - Hyperbolic Graph Embeddings

For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Brc7vN Jure Leskovec Computer Science, PhD In previous lectures, we focused on graph representation learning in Euclidean embedding spaces. In this lecture, we in

From playlist Stanford CS224W: Machine Learning with Graphs

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Tangent bundle | Perpendicular | Jacobian matrix and determinant | Stalk (sheaf) | Vector space | Product rule | Associative algebra | Pointwise product | Ideal (ring theory) | Zariski tangent space | Injective sheaf | Algebraic variety | Germ (mathematics) | Isomorphism | Complex manifold | Taylor's theorem | Map (mathematics) | Identity function | Inverse function theorem | Curve | Quotient space (linear algebra) | Coordinate-induced basis | Directional derivative | Local diffeomorphism | Exponential map (Riemannian geometry) | Differentiable manifold | Tangent vector | Linear map | Submanifold | Cotangent space | Equivalence class | Connected space | Mathematics | Dual space | Ordinary differential equation | Vector (mathematics and physics) | Sphere | Algebraic geometry | Embedding | Euclidean space | Local coordinates | Manifold | Equivalence relation | Ground field | Parallel transport | Differential geometry | Smoothness | Vector field | Open set