George Boole (1815-1864) was one of the forefathers of the Information Age and the first Professor of Mathematics at Queen's College Cork (now UCC). Computers, information storage and retrieval systems, electronic circuits and indeed the whole digital age depend on the simple but ingenious mathematical system he invented, Boolean Algebra. So it was fitting to have a George Boole Prize at BT Young Scientist and Technology Exhibition.
The exhibition is now in its 53rd year, making it one of the world’s longest standing events exhibiting secondary school students’ abilities in the areas of science and technology. The UCC George Boole Award for Excellence in Mathematics, sponsored by Arup, is one of numerous special awards presented at the BT Young Scientist and Technology Exhibition. The prize was awarded to the group that demonstrated the best use of mathematics in their project.
Prizewinners: Benedek Goz and Gleb Kurilenko are both in 3rd year studying for their Junior Certificate at Synge Street CBS, Dublin. Soon after they returned to school last August they saw a Young Scientist project report in their school library. It was written by Aleksander Kozina, a former pupil of Synge Street. Aleksander proved a number of new theorems using trilinear coordinates. In his report he suggested that many interesting theorems in Euclidean geometry could be proven using barycentric coordinates and he recommended more widespread use of the Kimberling Encyclopaedia of Triangle Centres.
The winning project, titled ‘Proving New Theorems Using Barycentric Coordinates’ involved students inputting barycentric coordinates into the dynamic geometry software program, Geogebra, to produce uncluttered diagrams and identify significant geometrical relationships. This project focuses on proving new theorems in Euclidean geometry by making use of barycentric coordinates.
Barycentric coordinates were invented by Möbius in 1827. Since then a great deal of research has been done by geometers to find formulas for the barycentric coordinates of the many special points of a triangle (the incentre, the circumcentre, the Nagel point, etc.).
We make use of the dynamic geometry software program Geogebra. We show how barycentric coordinates can be used in Geogebra. Their use allows us to obtain an uncluttered diagram free of construction lines. Finding the locations of the less well-known 'special points' often entails quite complex constructions; using barycentric coordinates is much quicker and less error-prone.
Careful visual exploration of a Geogebra worksheet will sometimes allow us to identify significant geometrical relationships. Such visual evidence does not, of course, constitute proof, no matter how convincing it may seem. Our proofs involve the use of barycentric coordinates obtained from Kimberling's Encyclopedia of Triangle Centres, some simple vector algebra and a little knowledge of determinants. We make use of the computer algebra system Derive to simplify some of the algebraic expressions that arise.
The prize was awarded in recognition of the project’s creativity and innovation, while making mathematics accessible and understandable to all.
Arup is delighted to continue sponsorship of this prize in the BT Young Scientist & Technology Exhibition, as it is vital to encourage young people to use mathematics to create solutions to the problems of tomorrow. Arup is dedicated to increasing the engagement of young people in science, technology, engineering and mathematics (STEM).