An astonishing piece of mathematical detective work has captured first prize in the 40th annual Esat BT Young Scientist and Technology Exhibition.
Dublin student Ronan Larkin of Synge Street Christian Brothers secondary school impressed the judges by devising an entirely new way to use repeating fractions for insoluble numbers such as pi.
Róisín McCloskey and Breandán Hill from Lumen Christi College in Derry claimed the best group project award with a study of "criticality", a subject related to chaotic behaviour.
The runner-up individual prize went to Patrick Collison of Castletroy College, Limerick, who wrote a computer programme that can teach itself English.
The runner-up group award went to Raymond Galligan, Christina Hannify and Angela Mulligan of Moyne Community School, Longford, for their study of teenage smoking.
The Minister for Education and Science, Mr Dempsey, last night announced the prizewinners at a spectacular ceremony at the RDS in Ballsbridge. Mr Dempsey and Esat BT and BT Northern Ireland chief executive, Mr Bill Murphy, presented Ronan Larkin with the Esat BT Young Scientist perpetual trophy and a cheque for €3,000.
Mr Dempsey praised the hard work put in by all the students, describing them as "unique", and paid tribute to the contribution made by both teachers and parents in helping the students complete their projects. He also praised the efforts made by the judges in selecting the winning projects.
The judges described Ronan Larkin's winning project, entitled "Generalised continued fractions", as "a superbly presented development of new techniques for solving difficult equations".
The 16-year-old fifth-year student used repeating algebraic fractions to prove that several formulas related to irrational numbers arising from equations such as the cubed root of two minus.
More importantly, he devised a continued fraction method for describing "transcendental numbers", for example the mathematical value pi and e, the base for natural logs. This he believes has never been accomplished before.
He will now also go forward to represent Ireland next September at the European Contest for Young Scientists, taking place here for the first time at UCD's Belfield campus.
The top group prize went to two Derry students for a project entitled "Self organised criticality in the dynamics of sandpiles", a study of how a growing sandpile can be brought to the point of collapse, known as criticality.
Róisín McCloskey (16) and Breandán Hill (17) revised and improved an existing software programme that could simulate the creation of an unstable sandpile, allowing them to simulate repeated runs towards criticality. They also invented a mechanical system to create real sandpiles, but using sesame seeds instead of sand grains. They received a trophy and a cheque for €1,500.
The runner-up individual award went to Patrick Collison (15), a third-year student for his "Isaac" computer programme, used in a project entitled "Emulating human response".
He produced the programme in an attempt to prove whether computers can be shown to have intelligence.
The programme starts with no understanding of natural language, but quickly learns through exchanges with humans. Patrick linked his programme to Internet chat rooms so it could pick up language use faster and, after 20 minutes, few in the chat room realised Isaac was not a human. He received a trophy and a cheque for €750.
Fifth-year students Raymond Galligan (16), Christina Hannify (16) and Angela Mulligan (17) claimed the runner-up group prize with their analysis of smoking cessation programmes in their project, "Teenager smokers - can they stop?" They found that while peer pressure might initiate smoking, peer support offered the most powerful way to help smokers stop.
The three conducted surveys amongst classmates to assess levels of smoking and rates of concealed smoking. They also assessed cessation programmes to decide which had greatest potential for success. The three receive a trophy and a cheque for €750.