When it comes to mathematical complexity it is difficult to top the dreaded pendulum on the end of an elastic band. The calculations that help predict where the weight will be at any given time are hellish.
Two sixth years from Christian Brothers Synge Street think they have the problem solved using some astoundingly difficult maths. Francis Wasser (16) and Michael Mulhall (17) had to reconstruct the differential equations first produced by Ireland's greatest scientist, William Rowan Hamilton, whose bicentennial is celebrated this year.
At its simplest, they were trying to devise a way to calculate where a pendulum might be after a given time once set in motion. To confirm the accuracy of their calculations they also wanted to determine the pendulum's energy level in that position.The work is ongoing but so far they have achieved very good results.
Nicola Kelly (15) and Shauna Maguire (15), third years from Our Lady's College, Drogheda, decided to pursue the magic of Kaprekar's Numbers. The Indian mathematician discovered an oddity. Take any three digits and use them to make the highest and lowest numbers possible. Subtract them to make a new three digit number then repeat this process using the new numbers. No matter what three you choose the answer will resolve to 495. If you use four digits the result will reach 6174.
Kaprekar used only base 10 numbers but Nicola and Shauna decided to expand the search, using bases 3 through 20 and anything from two to 15 digits.
Patterns emerged including the fact that any number in bases 3, 7 and 15 will resolve to zero.
