In metric geometry, the metric envelope or tight span of a metric space M is an injective metric space into which M can be embedded. In some sense it consists of all points "between" the points of M, analogous to the convex hull of a point set in a Euclidean space. The tight span is also sometimes known as the injective envelope or hyperconvex hull of M. It has also been called the injective hull, but should not be confused with the injective hull of a module in algebra, a concept with a similar description relative to the category of R-modules rather than metric spaces. The tight span was first described by , and it was studied and applied by in the 1960s. It was later independently rediscovered by and ; see for this history. The tight span is one of the central constructions of T-theory. (Wikipedia).
What is length contraction? Length contraction gives the second piece (along with time dilation) of the puzzle that allows us to reconcile the fact that the speed of light is constant in all reference frames.
From playlist Relativity
This knot is very useful for adjusting tie downs quickly and easily. For example, a tarp could be held down by a series of these knots and be made very tight so the wind cannot make it rise, and easily be removed simply by sliding the knots later. A taut line knot is also used to keep larg
From playlist Practical Projects & Skills
8.01x - Module 07.01 - Tension in a rope carrying a mass
Tension in a rope carrying a mass
From playlist 8.01x - MIT Help Sessions
Special Relativity C2 Length Contraction
Relativistic length contraction.
From playlist Physics - Special Relativity
Now You Know: Bursting Balloons
When you stick a needle in a balloon, the rubber tears—the balloon pops. But high-speed video reveals the details, and there are some surprises to be had. How does the rubber unzip as it tears? It’s different for a round balloon and a longer balloon-animal balloon. And if the balloon is fi
From playlist Now You Know
Special Relativity C3 Length Contraction
Relativistic length contraction.
From playlist Physics - Special Relativity
Rope Trick for my neighborhood
During my show, a rope is spotted in my sleeve. I pull it...
From playlist My Magic
Physics - Mechanics: Ch 17 Tension and Weight (1 of 11) What is Tension?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is tension and how to calculate tension using the free-body diagram. Next video in this series can be seen at: https://youtu.be/BxUhaktD8PA
From playlist PHYSICS MECHANICS 1: INTRO, VECTORS, MOTION, PROJECTILE MOTION, NEWTON'S LAWS
Lecture 3D - Lifting with a Pulley
Here is what pulleys are good for. They can apply the tension force multiple times for a "mechanical advantage". In this problem we go through the tensions and weights, and think about the effect on motion.
From playlist PHYS 125 | Forces
Facundo Mémoli: Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Title: Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius Abstract: The persistent homology induced by the Vietoris-Rips simplicial filtration is a standard method for capturing topological information from metric spaces. We consider a different, more geome
From playlist Vietoris-Rips Seminar
Viswanath Nagarajan: Approximation Friendly Discrepancy Rounding
We consider the general problem of rounding a fractional vector to an integral vector while (approximately) satisfying a number of linear constraints. Randomized rounding and discrepancy-based rounding are two of the strongest rounding methods known. However these algorithms are very diffe
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
Ulrich Bauer (3/4/22): Gromov hyperbolicity, geodesic defect, and apparent pairs in Rips filtrations
Motivated by computational aspects of persistent homology for Vietoris-Rips filtrations, we generalize a result of Eliyahu Rips on the contractibility of Vietoris-Rips complexes of geodesic spaces for a suitable parameter depending on the hyperbolicity of the space. We consider the notion
From playlist Vietoris-Rips Seminar
Seminar on Applied Geometry and Algebra (SIAM SAGA): Dustin Mixon
Title: Packing Points in Projective Spaces Speaker: Dustin Mixon Date: Tuesday, March 8, 2022 at 11:00am Eastern Abstract: Given a compact metric space, it is natural to ask how to arrange a given number of points so that the minimum distance is maximized. For example, the setting of the
From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)
On the number of ordinary lines determined by sets in complex space - Shubhangi Saraf
Computer Science/Discrete Mathematics Seminar I Topic: On the number of ordinary lines determined by sets in complex space Speaker: Shubhangi Saraf Affiliation: Rutgers University Date: December 5, 2016 For more video, visit http://video.ias.edu
From playlist Mathematics
A Fun Thing You Can Do With Topological Combinatorics
This video aims at explaining the connection between the Borsuk Ulam Theorem in topology and its connection with the Tucker's Lemma in the conbinatorics branch of math. The content is based on a direct reading program that took place from Feb. 2022 to Sep. 2022 in University of California,
From playlist Summer of Math Exposition 2 videos
⚠️ I have heard that YouTube might get rid of the comments section sometime next year. So that I can continue to answer your questions I created a Discord. I am available there basically all day to answer any questions you have about my videos. 🤗 MY DISCORD : https://discord.gg/pFkpxYC7r
From playlist Technical Analysis
A Constant-factor Approximation Algorithm for the Asymmetric Traveling Sale...- Ola Svensson
Computer Science/Discrete Mathematics Seminar II Topic: A Constant-factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem Speaker: Ola Svensson Affiliation: École polytechnique fédérale de Lausanne Date: January 23, 2018 For more videos, please visit http://video.ia
From playlist Mathematics
Animated Progress Bars: CSS Tutorial (Day 19 of CSS3 in 30 Days)
Create CSS only progress bars that animate. ⭐️Files you need ⭐️ 💻Animated Progress Bars Code: https://www.dropbox.com/sh/10fo07ed1d4d2x6/AAAvgjOOarwT-b6h5M7IVgSja?dl=0 💻All tutorials in this series need this "_theme-styles" directory (only download once): https://www.dropbox.com/sh/890hx6
From playlist CSS3 in 30 Days
Meltem Ünel: Height coupled trees
HYBRID EVENT Recorded during the meeting "Random Geometry" the January 20, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics
From playlist Probability and Statistics
Physics - Mechanics: Stress and Strain (2 of 16) Basics: Compression and Tensile
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the basics of compression stress and strain, and tensile stress and strain. The next video in this playlist: https://youtu.be/n7Z-lO3PGAc
From playlist PHYSICS 10.5 STRESS AND STRAIN