Ciara Ottewill is a stickler for accuracy, so she is unhappy with the typical "close" approximations used for the value of numbers like pi. She wanted the numbers to be more accurate yet easy to remember and so wrote a computer programme to get what she wanted. The result is a project with the challenging title, "Diophantine Approximation".
She presented the concepts behind approximating things such as the value of pi and the square root of two, and also offered very accurate alternatives to values familiar from school days, for example pi being equal to 22/7.
"I am slightly accuracy obsessed," the 15-year-old transition year student from Alexandra College, Milltown, admits. "Maths is my favourite subject and I want to do it in college."
Diophantus lived in Alexandra in the third century AD and was important in maths theory, Ciara explained. Pi and square root of two are known as irrational numbers and Diophantus developed ways to deliver good approximations of irrational numbers.
Ciara was interested in this, seeking very accurate approximations using fractions containing ordinary rational numbers. The goal was always to achieve the highest accuracy that can be reasonably achieved without having to use huge numbers, she explained. Students use 22/7 to approximate pi, but her computer programme showed that the fraction 355/113 is much more accurate when representing pi. It is also easy to remember, she said.
Her approximation for square root of two is the simple fraction 99/70.
