UK Unveils New Mathematical Phenomenon

28th June 2016. Exploring the mystery of the hexagon and the ‘Arokah’ effect.

A new concept which is set to spark global interest in the hexagon and its unique mathematical properties has been unveiled to the world for the first time – at a specialist education conference in the UK.

Discovered by Steve C Brazier, a maths teacher for almost 20 years, ‘Arokah’ featured at the STEMtech conference (Telford, 13 – 14th June 2016) as part of the official seminar programme with delegates being given the opportunity to explore the phenomenon in greater detail.

Known as ‘Arokah’, the discovery has identified an algorithm which produces 23 unique elements from a single hexagon. Consisting of both familiar and irregular shapes, the ‘Arokah’ effect is exclusively applicable to the hexagon.

Commenting on his mathematical breakthrough, Steve Brazier said: “I’ve been exploring the properties of a hexagon for well over 30 years now in a journey which started during my own time in the classroom. While trying to find increasingly creative and innovative ways to encourage students to investigate polygons it became apparent that the regular hexagon contained unique properties - sparking my naturally curious nature to investigate these further.”

Having talked publicly about ‘Arokah’ for the first time at STEMtech, Steve will now be visiting schools around the UK, educating students on the significance of the 23 individual elements and how these can be used to create a number of other pre-determined patterns, as determined by the mathematical algorithm. However, the underlying mathematical reasoning for the ‘Arokah’ effect, is at present, still unexplained. In the words of Prof. Imre Leader, University of Cambridge, Arokah is: “A NEW Mathematical Phenomenon”.  

Mathematicians, both those associated with the University of Cambridge and others, are as yet unable to offer an explanation. This has already stimulated interest in the academic community and led some researchers to use computers in a bid to better understand the phenomenon.

In addition to stimulating research ideas, ‘Arokah’ has already attracted interest from organisations who recognise its potential cognitive benefits. Steve continues: “Rather than Arokah simply being a mathematical theory, we’ve looked at how it can be used in practical teaching and development scenarios.

“As a tangible board with pieces, Arokah becomes a resource for developing skills such as spatial and logical reasoning, spatial awareness, strategic thinking and problem solving – all by using the unique properties of the Arokah shapes.”

These benefits are echoed by Charlie Stripp at the National Centre for the Excellence in the Teaching of Mathematics: “Arokah … really great for engaging children of all ages, both to help them appreciate the wonder of maths, and to support their learning of geometry and problem solving from the maths curriculum”.

More than a conceptual discovery, ‘Arokah’ will soon be available as a brainteaser board game. Launched in association with MENSA, to celebrate the organisation’s 70th anniversary later this year, pre-orders for Arokah can be made online at