Knot theory

Conway sphere

In mathematical knot theory, a Conway sphere, named after John Horton Conway, is a 2-sphere intersecting a given knot or link in a 3-manifold transversely in four points. In a knot diagram, a Conway sphere can be represented by a simple closed curve crossing four points of the knot, the cross-section of the sphere; such a curve does not always exist for an arbitrary knot diagram of a knot with a Conway sphere, but it is always possible to choose a diagram for the knot in which the sphere can be depicted in this way.A Conway sphere is essential if it is incompressible in the knot complement. Sometimes, this condition is included in the definition of Conway spheres. (Wikipedia).

Conway sphere
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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

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Generalized Conway Game of Life - SmoothLife4

Oscillatory structures are also possible.

From playlist SmoothLife

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Conway Cube Variations

another infinity cube

From playlist 3D printed toys

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A solar system, a simulation made with Excel

An Excel simulation of the solar system. You can see how things are recursively computed: the mutual gravity force from the locations, the accelerations, the velocities, and finally the updated locations. The solar eclipse is also shown. This is clip is intended to illustrate Chapter 24 Ap

From playlist Physics simulations

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Astronomy - Ch. 2: Understanding the Night Sky (5 of 23) Understanding the Celestial Sphere

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the celestial sphere (a sort of GPS of the universe).

From playlist ASTRONOMY 2 THE NIGHT SKY

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Studying Other Worlds with the Help of a Starshade

This animation shows the prototype starshade, a giant structure designed to block the glare of stars so that future space telescopes can take pictures of planets. More info here: http://planetquest.jpl.nasa.gov/video/15

From playlist Astrophysics

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Is the Conway knot slice? (After Lisa Piccirillo)

This is a talk on the recent work by Lisa Piccirillo showing that the Conway know is not a slice knot. We first review the definitions of the Conway know and slice knots, and then give an overview of her proof. The paper on this by Lisa Piccirillo can be found at https://arxiv.org/pdf/1

From playlist Math talks

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Allison Moore - Essential Conway spheres and Floer homology via immersed curves

38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Allison Moore, Virginia Commonwealth University Title: Essential Conway spheres and Floer homology via immersed curves Abstract: We consider the problem of whether Dehn surgery along a knot in the three-sphere produces an

From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021

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Sporadic groups

This is an informal talk on sporadic groups given to the Archimedeans (the Cambridge undergraduate mathematical society). It discusses the classification of finite simple groups and some of the sporadic groups, and finishes by briefly describing monstrous moonshine. For other Archimedeans

From playlist Math talks

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How to construct the Leech lattice

This lecture describes an astonishingly simple construction of the Leech lattice in 24 dimensions, found by John Conway and Neal Sloane. This is an experimental joint video with @Lyam Boylan (https://www.tiktok.com/@yamsox/video/7057530890381053189) who added the animation, the thumbnai

From playlist Math talks

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AlgTop19: An algebraic ZIP proof

We give a description of a variant to the proof of the Classification theorem for two dimensional combinatorial surfaces, due to John Conway and called the ZIP proof. Our approach to this is somewhat algebraic. We think about spheres with holes that are then zipped together rather than pol

From playlist Algebraic Topology: a beginner's course - N J Wildberger

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Teach Astronomy - Celestial Sphere

http://www.teachastronomy.com/ The celestial sphere is an imaginary sphere surrounding the Earth onto which are projected the objects of the night sky.  There are several fixed points on the celestial sphere that are important.  The Zenith is the point directly over your head.  The Nadir i

From playlist 02. Ancient Astronomy and Celestial Phenomena

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History of science 7: Did Witt discover the Leech lattice?

In about 1970 the German mathematician Witt claimed to have discovered the Leech lattice many years before Leech. This video explains what the Leech lattice is and examines the evidence for Witt's claim. Lieven Lebruyn discussed this question on his blog: http://www.neverendingbooks.org/w

From playlist History of science

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Questions and Answers 1

This is an experimental video where I give answers to the (mostly) mathematical questions asked by viewers.

From playlist Math talks

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Taut co-oriented foliations - Rachel Roberts

Rachel Roberts, WUSTL Workshop on Flows, Foliations and Contact Structures 2015-2016 Monday, December 7, 2015 - 08:00 to Friday, December 11, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academic

From playlist Workshop on Flows, Foliations and Contact Structures

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A Tour of Skein Modules by Rhea Palak Bakshi

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)

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Generalized Conway Game of Life - SmoothLifeC

with smooth time-stepping.

From playlist SmoothLife

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Sphere Investigation

Link: https://www.geogebra.org/m/D4hmNy9M

From playlist 3D: Dynamic Interactives!

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Drew Conway interviewed at Strata Summit 2011

Drew Conway PhD Student, New York University Drew Conway is a PhD student in political science at New York University. Drew studies terrorism and armed conflict; using tools from mathematics and computer science to gain a deeper understanding of these phenomena.

From playlist Strata NY 2011

Related pages

Incompressible surface | Transversality (mathematics) | 3-manifold | Knot complement | N-sphere | John Horton Conway | Knot theory