Folding Maps: A Simple but Unsolved Problem

Published February 14, 2019 Occasional Leave a Comment
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Paper-folding is a recurring theme in mathematics. The art of origami is much-loved by many who also enjoy recreational maths. One particular folding problem is remarkably easy to state, but the solution remains elusive:

Given a map with M × N panels, how many different ways can it be folded?

Each panel is considered to be distinct, so two foldings are equivalent only when they have the same vertical sequence of the L = M × N layers.

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Rambling and Reckoning

Published February 7, 2019 Irish Times Leave a Comment
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A walk on the beach, in the hills or along a river bank provides great opportunities for mathematical reflection. How high is the mountain? How many grains of sand are on the beach? How much water is flowing in the river?  [TM156 or search for “thatsmaths” at irishtimes.com].


Daily average flow (cubic metres per second) at Ardnacrusha, on the Shannon near Limerick. Data from the Electricity Supply Board (ESB).

While the exact answers may be elusive, we can make reasonable guesstimates using basic knowledge and simple mathematical reasoning. And we will be walking in the footsteps of some of the world’s greatest thinkers.

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Our Dearest Problems

Published January 31, 2019 Occasional 2 Comments
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A Colloquium on Recreational Mathematics took place in Lisbon this week. The meeting, RMC-VI (G4GEurope), a great success, was organised by the Ludus Association, with support from several other agencies: MUHNAC, ULisboa, CMAF-IO, CIUHCT, CEMAPRE, and FCT. It was the third meeting integrated in the Gathering for Gardner movement, which celebrates the great populariser of maths, Martin Gardner. For more information about the meeting, see http://ludicum.org/ev/rm/19 .

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From a Wide Wake to the Width of the World

Published January 24, 2019 Occasional Leave a Comment
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The finite angular width of a ship’s turbulent wake at the horizon enables the Earth’s radius to be estimated.

By ignoring evidence, Flat-Earthers remain secure in their delusions. The rest of us benefit greatly from accurate geodesy. Satellite communications, GPS navigation, large-scale surveying and cartography all require precise knowledge of the shape and form of the Earth and a precise value of its radius.


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Discoveries by Amateurs and Distractions by Cranks

Published January 17, 2019 Irish Times Leave a Comment
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Do amateurs ever solve outstanding mathematical problems? Professional mathematicians are aware that almost every new idea they have about a mathematical problem has already occurred to others. Any really new idea must have some feature that explains why no one has thought of it before  [TM155 or search for “thatsmaths” at irishtimes.com].

fermat-ramanujan

Pierre de Fermat and Srinivasa Ramanujan, two brilliant “amateur” mathematicians.

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Really, 0.999999… is equal to 1. Surreally, this is not so!

Published January 10, 2019 Occasional Leave a Comment
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The value of the recurring decimal 0.999999 … is a popular topic of conversation amongst amateur mathematicians of various levels of knowledge and expertise. Some of the discussions on the web are of little value or interest, but the topic touches on several subtle and deep aspects of number theory.

999999

[Image Wikimedia Commons]

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Trappist-1 & the Age of Aquarius

Published January 3, 2019 Irish Times Leave a Comment
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The Pythagoreans believed that the planets generate sounds as they move through the cosmos. The idea of the harmony of the spheres was brought to a high level by Johannes Kepler in his book Harmonices Mundi, where he identified many simple relationships between the orbital periods of the planets [TM154 or search for “thatsmaths” at irishtimes.com].

Artist’s impressions of the TRAPPIST-1 planetary system

Artist’s impression of the Trappist-1 planetary system. Image from https://www.eso.org/public/images/eso1805b/

Kepler’s idea was not much supported by his contemporaries, but in recent times astronomers have come to realize that resonances amongst the orbits has a crucial dynamical function. Continue reading ‘Trappist-1 & the Age of Aquarius’

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