Volume of an n-ball

Volume of a ball in n dimensions

In this video I explicitly calculate the volume of a ball of radius r in R^n. The method I’m presenting uses only multivariable calculus and the disk method from single-variable calculus, but we’ll also visit some other goodies like the Beta function and the Gamma function. Enjoy!

From playlist Calculus

Volume of a Sphere

This geometry video tutorial explains how to calculate the volume of a sphere. Geometry Playlist: https://www.youtube.com/watch?v=w8wdKOsUD-4&index=3&list=PL0o_zxa4K1BVkRxCZubMPcCJ5Q5QwZdEM Access to Premium Videos: https://www.patreon.com/MathScienceTutor Facebook: https://www.faceboo

From playlist Geometry Video Playlist

Volume of the Empty Space in a Cubic Box with a Ball Inside

This video explains how to determine the volume of the empty space in a cubic box with a ball inside. http://mathispower4u.com

From playlist Volume and Surface Area (Geometry)

Surface area of sphere in n dimensions

In this sequel to the video "Volume of a ball in n dimensions", I calculate the surface area of a sphere in R^n, using a clever trick with the Gaussian function exp(-1/2 |x|^2). Along the way, we discover the coarea formula, which is the analog of polar coordinates, but in n dimensions. Fi

From playlist Cool proofs

Introduction to Volume

This video introduces volume and shows how to determine the volume of a cube and rectangular solid. http://mathispower4u.com

From playlist Volume and Surface Area (Geometry)

Physics - Nuclear Physics (5 of 22) Volume of Earth as a Nuclear Ball

Visit http://ilectureonline.com for more math and science lectures! In this video I will show you how to find the volume of our Earth as a nuclear ball.

From playlist MODERN PHYSICS 2: ATOMIC AND NUCLEAR PHYSICS, PARTICLE PHYSICS

Capacity

From playlist h. Three-Dimensional Measurement

Volume of a sphere

Another practice problem dealing with the volume of a sphere

From playlist Middle School - Worked Examples

Determine the Volume of a Cube (Decimals)

This video explains how to determine the volume of a rectangular cube. http://mathispower4u.com

From playlist Volume and Surface Area (Geometry)

Reducing Isotropy to KLS: An Almost Cubic Volume Algorithm by Santosh Vempala

Program Advances in Applied Probability II (ONLINE) ORGANIZERS: Vivek S Borkar (IIT Bombay, India), Sandeep Juneja (TIFR Mumbai, India), Kavita Ramanan (Brown University, Rhode Island), Devavrat Shah (MIT, US) and Piyush Srivastava (TIFR Mumbai, India) DATE: 04 January 2021 to 08 Januar

From playlist Advances in Applied Probability II (Online)

Derivative of volume is surface area

In this neat video, I use the Divergence Theorem to show that, in any dimension, the derivative of the volume of a ball of radius r gives you the surface area of the sphere of radius r. So, for instance, it shouldn’t be surprising that (4/3 pi r^3)’ = 4pi r^2. The neat thing is that, at no

From playlist Multivariable Calculus

Santosh Vempala: Reducing Isotropy to KLS: An Almost Cubic Volume Algorithm

Computing the volume of a convex body is an ancient problem whose study has led to many interesting mathematical developments. In the most general setting, the convex body is given only by a membership oracle. In this talk, we present a faster algorithm for isotropic transformation of an a

From playlist Workshop: High dimensional measures: geometric and probabilistic aspects

How to Find a Random Point in a High Dimensional Ball #SoME2

My video for the SoME2 competition hosted by 3Blue1Brown. References: - Justin's video: "The BEST Way to Find a Random Point in a Circle" (https://www.youtube.com/watch?v=4y_nmpv-9lI&list=PLnQX-jgAF5pTkwtUuVpqS5tuWmJ-6ZM-Z&index=6&t=3s) - "Vector Calculus, Linear Algebra, and Differential

From playlist Summer of Math Exposition 2 videos

Ramon van Handel: The mysterious extremals of the Alexandrov-Fenchel inequality

The Alexandrov-Fenchel inequality is a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes. It is one of the central results in convex geometry, and has deep connections with other areas of mathematics. The characterization of its extremal bodie

From playlist Trimester Seminar Series on the Interplay between High-Dimensional Geometry and Probability

Metaphors in Systolic Geometry - Larry Guth

Larry Guth University of Toronto; Institute for Advanced Study October 18, 2010 The systolic inequality says that if we take any metric on an n-dimensional torus with volume 1, then we can find a non-contractible curve in the torus with length at most C(n). A remarkable feature of the ine

From playlist Mathematics

Stéphane Sabourau (4/1/22): Macroscopic scalar curvature and local collapsing

After introducing the notion of macroscopic scalar curvature, we will present the following result. Consider a Riemannian metric on a closed manifold admitting a hyperbolic metric. Suppose its macroscopic scalar curvature is greater or equal to the one of the hyperbolic metric. Then its vo

From playlist Vietoris-Rips Seminar

Gaussian Brunn-Minkowski Theory by Mokshay Madiman

PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab

From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY

Joscha Prochno: The large deviations approach to high-dimensional convex bodies, lecture III

Given any isotropic convex body in high dimension, it is known that its typical random projections will be approximately standard Gaussian. The universality in this central limit perspective restricts the information that can be retrieved from the lower-dimensional projections. In contrast

From playlist Workshop: High dimensional spatial random systems

Volume of a Cube

This geometry video tutorial explains how to calculate the volume of a cube. Geometry Playlist: https://www.youtube.com/watch?v=w8wdKOsUD-4&index=3&list=PL0o_zxa4K1BVkRxCZubMPcCJ5Q5QwZdEM Access to Premium Videos: https://www.patreon.com/MathScienceTutor Facebook: https://www.facebook.

From playlist Geometry Video Playlist