Total curvature

The Curvature of a Circle

The Curvature of a Circle

From playlist Calculus 3

What is Curvature? Calculus 3

What is Curvature? Calculus 3

From playlist Calculus 3

5 Curvature

The all important concept of curvature. We look at two equations for curvature and introduce the radius of curvature.

From playlist Life Science Math: Vectors

Curvature and Radius of Curvature for a function of x.

This video explains how to determine curvature using short cut formula for a function of x.

From playlist Vector Valued Functions

6C Second equation for curvature on the blackboard

In this lecture I show you a second equation for curvature.

From playlist Life Science Math: Vectors

Curvature for the general parabola | Differential Geometry 13 | NJ Wildberger

We now extend the discussion of curvature to a general parabola, not necessarily one of the form y=x^2. This involves first of all understanding that a parabola is defined projectively as a conic which is tangent to the line at infinity. We find the general projective 3x3 matrix for suc

From playlist Differential Geometry

Gauss Curvature

Reference: Differential Geometry by Do Carmo My first video! Thank you for coming and any suggestion is very welcomed! #some2

From playlist Summer of Math Exposition 2 videos

Curvature and Radius of Curvature for 2D Vector Function

This video explains how to determine curvature using short cut formula for a vector function in 2D.

From playlist Vector Valued Functions

Bobo Hua (7/27/22): Curvature conditions on graphs

Abstract: We will introduce various curvature notions on graphs, including combinatorial curvature for planar graphs, Bakry-Emery curvature, and Ollivier curvature. Under curvature conditions, we prove some analytic and geometric results for graphs with nonnegative curvature. This is based

From playlist Applied Geometry for Data Sciences 2022

The second most beautiful equation and its surprising applications

Get free access to over 2500 documentaries on CuriosityStream: https://curiositystream.com/majorprep (use promo code "majorprep" at sign up) STEMerch Store: https://stemerch.com/ Support the Channel: https://www.patreon.com/zachstar PayPal(one time donation): https://www.paypal.me/ZachStar

From playlist Applied Math

Curvature of a Riemannian Manifold | Riemannian Geometry

In this lecture, we define the exponential mapping, the Riemannian curvature tensor, Ricci curvature tensor, and scalar curvature. The focus is on an intuitive explanation of the curvature tensors. The curvature tensor of a Riemannian metric is a very large stumbling block for many student

From playlist All Videos

AlgTop16: Rational curvature of polytopes and the Euler number

We show that the total curvature of a polyhedron is equal to its Euler number. This only works with the rational formulation of curvature, using an analog of the turn angle suitable for the 2 dimensional sphere. This important modification to the theory is original with this lecture series

From playlist Algebraic Topology: a beginner's course - N J Wildberger

Yuguang Shi - Quasi-local mass and geometry of scalar curvature

Quasi-local mass is a basic notion in General Relativity. Geometrically, it can be regarded as a geometric quantity of a boundary of a 3-dimensional compact Riemannian manifold. Usually, it is in terms of area and mean curvature of the boundary. It is interesting to see that some of quasi

From playlist Not Only Scalar Curvature Seminar

Bifurcating conformal metrics with constant Q-curvature - Renato Bettiol

More videos on http://video.ias.edu

From playlist Variational Methods in Geometry

Lecture 16: Discrete Curvature I (Discrete Differential Geometry)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg

From playlist Discrete Differential Geometry - CMU 15-458/858

Lecture 17: Discrete Curvature II (Discrete Differential Geometry)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg

From playlist Discrete Differential Geometry - CMU 15-458/858

Bernhard Hanke - Surgery, bordism and scalar curvature

One of the most influential results in scalar curvature geometry, due to Gromov-Lawson and Schoen-Yau, is the construction of metrics with positive scalar curvature by surgery. Combined with powerful tools from geometric topology, this has strong implications for the classification of suc

From playlist Not Only Scalar Curvature Seminar

Lecture 15: Curvature of Surfaces (Discrete Differential Geometry)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg

From playlist Discrete Differential Geometry - CMU 15-458/858

Curvature formula, part 1

Curvature is computed by first finding a unit tangent vector function, then finding its derivative with respect to arc length. Here we start thinking about what that means.

From playlist Multivariable calculus

Chao Li - Scalar curvature and the dihedral rigidity conjecture

In 2013, Gromov proposed a geometric comparison theorem for metrics with nonnegative scalar curvature, formulated in terms of the dihedral rigidity phenomenon for Riemannian polyhedrons. In this talk, I will discuss recent progress towards this conjecture, and its connection to other rigid

From playlist Not Only Scalar Curvature Seminar