Steiner’s minimal tree problem is this: **Find the shortest possible network interconnecting a set of points in the Euclidean plane.** If the points are linked directly to each other by straight line segments, we obtain the *minimal spanning tree*. But Steiner’s problem allows for additional points – now called Steiner points – to be added to the network, yielding *Steiner’s minimal tree*. This generally results in a reduction of the overall length of the network.

## Archive for January, 2015

### The Steiner Minimal Tree

Published January 29, 2015 Occasional Leave a CommentTags: Algebra, Algorithms, Gauss, Maps, Topology

### Plateau’s Problem and Double Bubbles

Published January 22, 2015 Occasional Leave a CommentTags: Algorithms, Fluid Dynamics, Physics, Topology

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].

### Barcodes and QR Codes: Zebra stripes and Leopard spots

Published January 15, 2015 Irish Times Leave a CommentTags: Algorithms, Computer Science

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).

Continue reading ‘Barcodes and QR Codes: Zebra stripes and Leopard spots’

### Seifert Surfaces for Knots and Links.

Published January 8, 2015 Occasional Leave a CommentTags: Geometry, Topology

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.

Continue reading ‘Seifert Surfaces for Knots and Links.’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.

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

37,000times 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.

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