Posts Tagged 'Topology'

Stan Ulam, a mathematician who figured how to initiate fusion

Published May 3, 2018 Irish Times Leave a Comment
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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].

Thermonuclear-Explosion

Operation Castle, Bikini Atoll, 1954

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Moebiquity: Ubiquity and Versitility of the Möbius Band

Published January 11, 2018 Occasional Leave a Comment
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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.

Mobius-Curved-Flat

Möbius band in 3-space and a flat representation in 2-space.

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Disentangling Loops with an Ambient Isotopy

Published November 30, 2017 Occasional Leave a Comment
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Linked-Loops-1

Can one of these shapes be continuously distorted to produce the other?

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 Comment
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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.

Recycling-Symbol-2Verions

Original (Moebius) and a variation (3-twist) of the universal recycling symbol.

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Building Moebius Bands

Published September 28, 2017 Occasional Leave a Comment
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We are all familiar with the Möbius strip or Möbius band. This topologically intriguing object with one side and one edge has fascinated children of all ages since it was discovered independently by August Möbius and Johann Listing in the same year, 1858.

MobiusBuild-00

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Topology in the Oval Office

Published February 23, 2017 Occasional Leave a Comment
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Imagine a room – the Oval Office for example – that has three electrical appliances:

•  An air-conditioner ( a ) with an American plug socket ( A ),

•  A boiler ( b ) with a British plug socket ( B ),

•  A coffee-maker ( c ) with a Continental plug socket ( C ).

The problem is to connect each appliance to the correct socket, avoiding any crossings of the connecting wires.

electricplugs-01

Fig. 1: Positions of appliances and sockets for Problem 1.

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The Library of Babel and the Information Explosion

Published January 19, 2017 Irish Times Leave a Comment
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The world has been transformed by the Internet. Google, founded just 20 years ago, is a major force in online information. The company name is a misspelt version of “googol”, the number one followed by one hundred zeros. This name echoes the vast quantities of information available through the search engines of the company [TM107 or search for “thatsmaths” at irishtimes.com].

libraryofbabel

Artist’s impression of the Library of Babel [Image from Here].

Long before the Internet, the renowned Argentine writer, poet, translator and literary critic Jorge Luis Borges (1889 – 1986) envisaged the Universe as a vast information bank in the form of a library. The Library of Babel was imagined to contain every book that ever was or ever could be written.

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