Soon it will be time to pack away the fairy lights. If you wish to avoid the knotty task of disentangling them next December, don’t just throw them in a box; roll them carefully around a stout stick or a paper tube. Any long and flexible string or cable, squeezed into a confined volume, is likely to become entangled: just think of garden hoses or the wires of headphones [TM178 or search for “thatsmaths” at irishtimes.com].

## Posts Tagged 'Topology'

### The knotty problem of packing DNA

Published January 2, 2020 Irish Times Leave a CommentTags: biology, Topology

### Simple Curves that Perplex Mathematicians and Inspire Artists

Published June 20, 2019 Irish Times Leave a CommentTags: Algorithms, Topology

The preoccupations of mathematicians can seem curious and strange to *normal* people. They sometimes expend great energy proving results that appear glaringly obvious. One such result is called the **Jordan** **Curve** **Theorem**. We all know that a circle has an inside and an outside, and that this property also holds for a much larger collection of closed curves [TM165 or search for “thatsmaths” at irishtimes.com].

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### Consider a Spherical Christmas Tree

Published December 20, 2018 Irish Times Leave a CommentTags: Algorithms, Topology

A minor seasonal challenge is how to distribute the fairy lights evenly around the tree, with no large gaps or local clusters. Since the lights are strung on a wire, we are not free to place them individually but must weave them around the branches, attempting to achieve a pleasing arrangement. Optimization problems like this occur throughout applied mathematics [TM153 or search for “thatsmaths” at irishtimes.com].

Trees are approximately conical in shape and we may assume that the lights are confined to the surface of a cone. The peak, where the Christmas star is placed, is a mathematical singularity: all the straight lines that can be drawn on the cone, the so-called generators, pass through this point. Cones are *developable* surfaces: they can be flattened out into a plane without being stretched or shrunk.

### Stan Ulam, a mathematician who figured how to initiate fusion

Published May 3, 2018 Irish Times Leave a CommentTags: Algorithms, Fluid Dynamics, Set Theory, Topology

Stanislaw Ulam, born in Poland in 1909, was a key member of the remarkable Lvov School of Mathematics, which flourished in that city between the two world wars. Ulam studied mathematics at the Lvov Polytechnic Institute, getting his PhD in 1933. His original research was in abstract mathematics, but he later became interested in a wide range of applications. He once joked that he was “a pure mathematician who had sunk so low that his latest paper actually contained numbers with decimal points” [TM138 or search for “thatsmaths” at irishtimes.com].

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### Moebiquity: Ubiquity and Versitility of the Möbius Band

Published January 11, 2018 Occasional Leave a CommentTags: Topology

The Möbius strip or Möbius band, with one side and one edge, has been a source of fascination since its discovery in 1858, independently by August Möbius and Johann Listing. It is easily formed from a strip of paper by giving it a half-twist before joining the ends.

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### Disentangling Loops with an Ambient Isotopy

Published November 30, 2017 Occasional Leave a CommentTags: Topology

The surface in the left panel above has two linked loops. In the right hand panel, the loops are unlinked. Is it possible to continuously distort the left-hand surface so as to unlink the loops and produce the right-hand figure? This seems impossible, but intuition is not always reliable.

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### A Symbol for Global Circulation

Published November 23, 2017 Occasional Leave a CommentTags: Geometry, Topology

The recycling symbol consisting of three bent arrows is found on bottles, cartons and packaging of all kinds. It originated in 1970 when the Chicago-based Container Corporation of America (CCA) held a competition for the design of a symbol suitable for printing on cartons, to encourage recycling and re-use of packaging materials.