In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus. If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a toroid, as in a square toroid. Real-world objects that approximate a torus of revolution include swim rings, inner tubes and ringette rings. Eyeglass lenses that combine spherical and cylindrical correction are toric lenses. A torus should not be confused with a solid torus, which is formed by rotating a disk, rather than a circle, around an axis. A solid torus is a torus plus the volume inside the torus. Real-world objects that approximate a solid torus include O-rings, non-inflatable lifebuoys, ring doughnuts, and bagels. In topology, a ring torus is homeomorphic to the Cartesian product of two circles: S1 × S1, and the latter is taken to be the definition in that context. It is a compact 2-manifold of genus 1. The ring torus is one way to embed this space into Euclidean space, but another way to do this is the Cartesian product of the embedding of S1 in the plane with itself. This produces a geometric object called the Clifford torus, a surface in 4-space. In the field of topology, a torus is any topological space that is homeomorphic to a torus. The surface of a coffee cup and a doughnut are both topological tori with genus one. An example of a torus can be constructed by taking a rectangular strip of flexible material, for example, a rubber sheet, and joining the top edge to the bottom edge, and the left edge to the right edge, without any half-twists (compare Möbius strip). (Wikipedia).
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
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
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" 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 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
necklace,two way,Torus by Villarceau circles,mobius ball
From playlist Handmade geometric 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
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
From playlist Surface integrals
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
Chapter 8 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
L14.2 Quantization of the magnetic field on a torus
MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L14.2 Quantization of the magnetic field on a torus License: Creative Com
From playlist MIT 8.06 Quantum Physics III, Spring 2018
The Assassin Puzzle | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Imagine you have a square-shaped room, and inside there is an assassin and a target. And suppose that any shot that the assassin takes can ricochet off the walls of the
From playlist An Infinite Playlist
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
A Continuous Transformation of a Double Cover of the Complex Plane into a Torus
To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technology-conference/ Speaker: Dominic Milioto Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, a
From playlist Wolfram Technology Conference 2017
This week’s video is about the beautiful mathematics you encounter when you try to turn ghostlike closed surfaces inside out. Learn about the mighty double Klein bottle trick, be one of the first to find out about a fantastic new way to turn a sphere inside out and have another go at earni
From playlist Recent videos
Mirror symmetry and cluster algebras – Paul Hacking & Sean Keel – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.15 Mirror symmetry and cluster algebras Paul Hacking & Sean Keel Abstract: We explain our proof, joint with Mark Gross and Maxim Kontsevich, of conjectures of Fomin–Zelevinsky and Fock–Goncharov on canonical bases of cluster algebras. We i
From playlist Algebraic & Complex Geometry
Supercuspidal L-packets - Tasho Kaletha
Computer Science/Discrete Mathematics Seminar I Topic: Supercuspidal L-packets Speaker: Tasho Kaletha Affiliation: Technion Date: March 5, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Conway's Game of Life on a Torus
Conway's Life rule is often run on a flat grid with wrap-around. Here we do the same thing but with the sides joined together to make an actual 3D torus. Generated with open source software: http://code.google.com/p/reaction-diffusion/
From playlist Ready
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