A home schooled teenager from Danville has won himself $100,000, and even got to meet the President of the United States. If you think that sounds pretty sweet, maybe you too should learn how to solve a problem involving “Continued Fraction Convergents and Linear Fractional Transformations” – in general terms.
Evan O’Dorney won the Intel Science Talent Search, a national competition that attracts top students from all over the country. After being short listed into a an elite group of 40 students, O’Dorney got to meet the President along with the other top contestants in an all expenses-paid trip to the nation’s capital.
However, that particular meeting was unlikely to phase the young O’Dorney, who has had previous meetings with President Obama and President George W. Bush when he won the American Mathematical Society’s “Who Wants to Be a Mathematician?” and the Scripps National Spelling Bee respectively.
“I’m getting pretty comfortable with it by now,” he said of his recurring fame. In order to win his latest prize, O’Dorney submitted a complex maths problem which involved square roots. While he was not the only contestant to solve the problem, he was the only one who managed to do it in general terms.
In the problem summary O’Dorney wrote: “Many methods exist for approximating the value of a square root by ordinary fractions, including the venerable method of continued fractions (hereafter called Method I) and the newer method of iterating a linear fractional transformation (Method II)… In this project, I have discovered and proved an unexpectedly simple formula that allows one to predict, given a particular square root, whether the two methods yield infinitely many results in common.”
It was not a quick problem to solve however, with O’Dorney saying “It was a year before I was able to work it specifically, and several months before I generalised and specified. I just had to stick with it.” It seems that even the smartest people out there also need to be persistent if they want to experience true success.