Posts Tagged 'Recreational Maths'

Spiralling Primes


The Sacks Spiral.

The prime numbers have presented mathematicians with some of their most challenging problems. They continue to play a central role in number theory, and many key questions remain unsolved.

Order and Chaos

The primes have many intriguing properties. In his article “The first 50 million prime numbers”, Don Zagier noted two contradictory characteristics of the distribution of prime numbers. The first is the erratic and seemingly chaotic way in which the primes “grow like weeds among the natural numbers”. The second is that, when they are viewed in the large, they exhibit “stunning regularity”.

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Learning Maths without even Trying

Children have an almost limitless capacity to absorb knowledge if it is presented in an appealing and entertaining manner. Mathematics can be daunting, but it is possible to convey key ideas visually so that they are instantly accessible. Visiting Explorium recently, I saw such a visual display demonstrating the theorem of Pythagoras, which, according to Jacob Bronowski, “remains the most important single theorem in the whole of mathematics” [TM167 or search for “thatsmaths” at].


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Rambling and Reckoning

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].

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

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 .

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Discoveries by Amateurs and Distractions by Cranks

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].


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

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Tom Lehrer: Comical Musical Mathematical Genius


Tom Lehrer, mathematician, singer, songwriter and satirist, was born in New York ninety years ago. He was active in public performance for about 25 years from 1945 to 1970. He is most renowned for his hilarious satirical songs, many of which he recorded and which are available today on YouTube [see TM147, or search for “thatsmaths” at].

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Kaprekar’s Number 6174

The Indian mathematician D. R. Kaprekar spent many happy hours during his youth solving mathematical puzzles. He graduated from Fergusson College in Pune in 1929 and became a mathematical teacher at a school in Devlali, north-east of Mumbai.


Kaprekar process for three digit numbers converging to 495 [Wikimedia Commons].

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