We know, thanks to Georg Cantor, that the rational numbers — ratios of integers — are countable: they can be put into one-to-one correspondence with the natural numbers.

Continue reading ‘Listing the Rational Numbers: I. Farey Sequences’

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Tags: Arithmetic, Number Theory

We know, thanks to Georg Cantor, that the rational numbers — ratios of integers — are countable: they can be put into one-to-one correspondence with the natural numbers.

Continue reading ‘Listing the Rational Numbers: I. Farey Sequences’

Tags: Education, Music, Recreational Maths

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 irishtimes.com].

Continue reading ‘Tom Lehrer: Comical Musical Mathematical Genius’

Tags: Geometry

Walking in Hyde Park recently, I spied what appeared to be a huge red pyramid in the middle of the Serpentine. On closer approach, and with a changing angle of view, it became clear that it was prismatic in shape, composed of numerous barrels in red, blue and purple.

Tags: Algorithms, Computer Science, Social attitudes

As you pass through an airport, you are photographed several times by security systems. Face recognition systems can identify you by comparing your digital image to faces stored in a database. This form of identification is gaining popularity, allowing you to access online banking without a PIN or password. [see TM146, or search for “thatsmaths” at irishtimes.com].