Plateau’s Problem and Double Bubbles

Bubbles floating in the air strive to achieve a spherical form. Large bubbles may oscillate widely about this ideal whereas small bubbles quickly achieve their equilibrium shape. The sphere is optimal: it encloses maximum volume for any surface of a given area. This was stated by Archimedes, but he did not have the mathematical techniques required to prove it. It was only in the late 1800s that a formal proof of optimality was completed by Hermann Schwarz [Schwarz, 1884].

Computer-generated double bubble

Computer-generated double bubble

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Barcodes and QR Codes: Zebra stripes and Leopard spots

Barcodes and QR codes are described in this week’s That’s Maths column in The Irish Times (TM060, or search for “thatsmaths” at irishtimes.com).

EAN-13 barcode.

EAN-13 barcode.

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Seifert Surfaces for Knots and Links.

We are all familiar with knots. Knots keep our boats securely moored and enable us to sail across the oceans. They also reduce the cables and wires behind our computers to a tangled mess. Many fabrics are just complicated knots of fibre and we know how they can unravel.

From left to right: Figure-of-8 knot 4_1, knot 6_3 , knot 7_1, and knot 8_5 [Fig from Van Wijk (2006)].

From left to right: Figure-of-8 knot 4_1, knot 6_3 , knot 7_1, and knot 8_5 [Drawn with SeifertView (image from Van Wijk, 2006)].

Continue reading ‘Seifert Surfaces for Knots and Links.’

The MacTutor Archive

The MacTutor History of Mathematics archive is a website hosted by the University of St Andrews in Scotland. It was established, and is maintained, by Dr John O’Connor and Prof Edmund Robertson of the School of Mathematics and Statistics at St Andrews.

MacTutor contains biographies of a large number of mathematicians, both historical and contemporary. In many cases, the Wikipedia entry on a mathematician directs to MacTutor for more complete biographical information.

Screen image of the MacTutor page listing History Topics.

Screen image of the MacTutor page listing History Topics.

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2014 in review

2014 annual report of WordPress.com for this blog.

Here’s an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 37,000 times in 2014. If it were a concert at Sydney Opera House, it would take about 14 sold-out performances for that many people to see it.

Click here to see the complete report.

Fermat’s Christmas Theorem

Albert Girard (1595-1632) was a French-born mathematician who studied at the University of Leiden. He was the first to use the abbreviations ‘sin’, ‘cos’ and ‘tan’ for the trigonometric functions.

Left: Albert Girard (1595-1632). Right: Pierre de Fermat (1601-1665)

Left: Albert Girard (1595-1632). Right: Pierre de Fermat (1601-1665)

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Information Theory

That’s Maths in The Irish Times this week (TM059, or Search for “thatsmaths” at irishtimes.com) is about data compression and its uses in modern technology.

Left: An equation form Shannon (1948), the paper that launched Information Theory.  Right: Claude Shannon (1916-2001) ©Alcatel-Lucent.

Left: An equation form Shannon (1948), the paper that launched Information Theory.
Right: Claude Shannon (1916-2001) ©Alcatel-Lucent.

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