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 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
What is General Relativity? Lesson 68: The Einstein Tensor
What is General Relativity? Lesson 68: The Einstein Tensor The Einstein tensor defined! Using the Ricci tensor and the curvature scalar we can calculate the curvature scalar of a slice of a manifold using the Einstein tensor. Please consider supporting this channel via Patreon: https:/
From playlist What is General Relativity?
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
F. Schulze - Mean curvature flow with generic initial data (version temporaire)
Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric heat equation on the space of hypersurfaces in an ambient Riemannian manifold. It is believed, similar to Ricci Flow in the intrinsic setting, to have the potential to serve as a tool to app
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
6D Third equation for curvature on the blackboard
In this video I introduce a third equation for curvature. Now you know them all.
From playlist Life Science Math: Vectors
Astronomy: The Big Bang (28 of 30) Curvature of the Universe
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain why and how the curvature of the universe came about.
From playlist ASTRONOMY 25 THE BIG BANG
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
Jürgen Jost (5/13/22): Geometry and Topology of Data
We link the basic concept of topological data analysis, intersection patterns of distance balls, with geometric concepts. The key notion is hyperconvexity, and we also explore some variants. Hyperconvexity in turn leads us to a new concept of generalized curvature for metric spaces. Curvat
From playlist Bridging Applied and Quantitative Topology 2022
Emily Stark: The visual boundary of hyperbolic free-by-cyclic groups
Abstract: Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, th
From playlist Topology
Recognising Fractals from a reasonable distance - Linear Distance Estimation Edition!
Welcome to the second part of the series on recognising fractals from a reasonable distance! This is the Linear Distance Estimation Edition, featuring the following fractals: Amazing box - Mod 2 Abox - Mod Kali-V3 Abox - SurfBox Generalized Fold Box - Octahedron Generalized Fold Box - Oc
From playlist Nerdy Rodent Uploads!
The Million Dollar Problem that Went Unsolved for a Century - The Poincaré Conjecture
Topology was barely born in the late 19th century, but that didn't stop Henri Poincaré from making what is essentially the first conjecture ever in the subject. And it wasn't any ordinary conjecture - it took a hundred years of mathematical development to solve it using ideas so novel that
From playlist Math
Coding Challenge #2: Menger Sponge Fractal
In this coding challenge, I attempt to code the Menger Sponge (fractals) using Processing. Code: https://thecodingtrain.com/challenges/2-menger-sponge 🕹️ p5.js Web Editor Sketch: https://editor.p5js.org/codingtrain/sketches/5kcBUriAy 🎥 Previous video: https://youtu.be/17WoOqgXsRM?list=PL
From playlist Coding Challenges
Cong He: Right-angled Coxeter Groups with Menger Curve Boundary
Cong He, University of Wisconsin Milwaukee Title: Right-angled Coxeter Groups with Menger Curve Boundary Hyperbolic Coxeter groups with Sierpinski carpet boundary was investigated by {\'S}wi{\c{a}}tkowski. And hyperbolic right-angled Coxeter group with Gromov boundary as Menger curve was s
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
GCSE Maths: Volume of 3D Shapes Livestream
The third of six livestreams happening every Friday at 4pm (GMT +1) discussing the topics of the Tom Rocks Maths Appeal GCSE Maths series. The topic this week is the Volume of 3D shapes (Cubes, Cuboids, Prisms and Cylinders) - full list of questions discussed (with timestamps) below. How
From playlist Tom Rocks GCSE Maths Appeal
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
Live Stream #31: Shape Morphing and Menger Sponge in Processing
Live from sfpc.io! In this video, using Processing, I take on two chat submitted challenges: Shape morphing and the Menger sponge (fractals). 15:07 - Challenge #1: Shape Morphing 44:30 - Preparation for the 2nd challenge 53:14 - Challenge #2: Menger Sponge 1:17:40 - Picking up after tec
From playlist Live Stream Archive
Lecture 20 - Trees and Connectivity
This is Lecture 20 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2020.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
Intro to Menger's Theorem | Graph Theory, Connectivity
Menger's theorem tells us that for any two nonadjacent vertices, u and v, in a graph G, the minimum number of vertices in a u-v separating set is equal to the maximum number of internally disjoint u-v paths in G. The Proof of Menger's Theorem: https://youtu.be/2rbbq-Mk-YE Remember that
From playlist Graph Theory
#Physics #Mechanics #Engineering #NicholasGKK #Shorts
From playlist General Mechanics