Geometric topology | Differential geometry | 3-manifolds | Topology | Differential topology

The three-dimensional torus, or 3-torus, is defined as any topological space that is homeomorphic to the Cartesian product of three circles, In contrast, the usual torus is the Cartesian product of only two circles. The 3-torus is a three-dimensional compact manifold with no boundary. It can be obtained by "gluing" the three pairs of opposite faces of a cube, where being "glued" can be intuitively understood to mean that when a particle moving in the interior of the cube reaches a point on a face, it goes through it and appears to come forth from the corresponding point on the opposite face, producing periodic boundary conditions. Gluing only one pair of opposite faces produces a solid torus while gluing two of these pairs produces the solid space between two nested tori. In 1984, Alexei Starobinsky and Yakov Borisovich Zel'dovich at the Landau Institute in Moscow proposed a cosmological model where the shape of the universe is a 3-torus. (Wikipedia).

Buy at http://www.shapeways.com/shops/GeometricToy "Torus Magic" can eat another torus.This torus object is constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,AkiraNishihara

From playlist 3D printed toys

necklace,two way,Torus by Villarceau circles,mobius ball

From playlist Handmade geometric toys

Buy at http://www.shapeways.com/shops/GeometricToy "Torus Magic" can eat another torus.This torus object is constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,AkiraNishihara

From playlist 3D printed toys

Buy at http://www.shapeways.com/shops/GeometricToy Torus Magic is a transformable torus. This torus object is constructed with many rings,and transforms flat,spherical etc. Also you can turn inside out the torus. Copyright (c) 2014,AkiraNishihara

From playlist 3D printed toys

The torus magic is constructed with many rings. It transforms flat,spherical,etc. Farther more you can turn it inside out.

From playlist Handmade geometric toys

Buy at http://www.shapeways.com/shops/GeometricToy Torus Magic is a transformable torus. This torus object is constructed with 20 large rings(50mm diameter) and many small rings.It transforms flat,spherical etc. Also you can turn inside out the torus. Copyright (c) 2015,AkiraNishihara

From playlist 3D printed toys

Buy at http://www.shapeways.com/shops/GeometricToy This object consists of two "Torus Magic".These torus objects are constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,Akira Nishihara

From playlist 3D printed toys

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/KiL

From playlist 3D printing

Toroflux paradox: making things (dis)appear with math

NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) Today is all about geometric appearing and vanishing paradoxes and that math that powers them. This vide

From playlist Recent videos

Chapter 8 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

Nonlinear algebra, Lecture 7: "Toric Varieties", by Mateusz Michalek

This is the seventh lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.

From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

Random walks on Tori and normal numbers in self similar sets by Arijit Ganguly

PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.

From playlist Smooth And Homogeneous Dynamics

Telling Time on a Torus | Infinite Series

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi What shape do you most associate with a standard analog clock? Your reflex answer might be a circle, but a more natural answer is actually a torus. Surprised? Then stic

From playlist An Infinite Playlist

Hyperbolic Knot Theory (Lecture - 2) by Abhijit Champanerkar

PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl

From playlist Knots Through Web (Online)

What are minimal surfaces? by Rukmini Dey

PROGRAM : SUMMER SCHOOL FOR WOMEN IN MATHEMATICS AND STATISTICS ORGANIZERS : Siva Athreya and Anita Naolekar DATE & TIME : 07 May 2018 to 18 May 2018 VENUE : Ramanujan Lecture Hall, ICTS Bengaluru The summer school is intended for women students studying in first year B.Sc./B.E./B.Tech

From playlist Summer School for Women in Mathematics and Statistics - 2018

The Poincaré Conjecture (special lecture) John W. Morgan [ICM 2006]

slides for this talk: https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/tars/morgan2006.pdf The Poincaré Conjecture (special lecture) John W. Morgan Columbia University, USA https://www.mathunion.org/icm/icm-videos/icm-2006-videos-madrid-spain/icm-madrid-videos-24082006

From playlist Mathematics

Physics - Mechanics: Torsion (1 of 14) What is Torsion?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is torsion and the variables associated with twisting of a steel rod. Next video in this series can be found at: https://youtu.be/jlt6Jy59nJs

From playlist PHYSICS 16.6 TORSION

Andrew Lobb: Quantum sln knot cohomology and the slice genus

Abstract: We will give an overview of the information about the smooth slice genus so far yielded by the quantum 𝔰𝔩n knot cohomologies. Recording during the thematic meeting "Knotted Embeddings in Dimensions 3 and 4" the February 15, 2017 at the Centre International de Rencontres Mathémat

From playlist Topology