Thursday, 13 June 2013 00:00
North High School sophomore Daniel Hanover took a third place Mathematical Sciences Award at the Intel International Science and Engineering Fair (ISEF), held in Phoenix, Arizona, for his project, “Kaprekar’s Constant: A Journey into New Bases.” Daniel had been a finalist at the Long Island Science and Engineering Fair, which qualified him to compete at ISEF. Over 1,500 high school students, from some 70 countries, regions, and territories, vied for top awards at ISEF. Contestants were required to do extensive research and persuasively present their findings on an advanced mathematical topic to doctoral-level scientists.
Daniel explained his project in his research project abstract: “The number 6174 has arisen as a famous solution to a problem of multiple steps. First, take any four-digit number that has at least two distinct digits. Then, rearrange the digits of the original number in ascending and descending order, take these two numbers, and find the difference between the two. Finally, repeat this routine using the difference as the new four-digit number. In 1949, Dattaraya Ramchandra Kaprekar, an Indian mathematician, was the first to discover that this process, sometimes called ‘Kaprekar Routine,’ would always yield 6174 within seven repetitions. Since this number remains unchanged after an application of Kaprekar Routine, it became known as ‘Kaprekar’s Constant.’ Previous works have shown that the only base-10 Kaprekar’s Constants are 495 and 6174. However, little attention has been given to other bases or figuring out which digits and which bases actually have a Kaprekar’s Constant.” Daniel extended the scope through which Kaprekar’s Constant is viewed by “establishing laws for other bases and digits regarding the properties of their respective Kaprekar’s Constant.” In addition, he explained why these laws occur and what they could indicate.
Daniel began his math research project last year, under the guidance of science teacher Alan Schorn, and continued it this year under Schorn and science teacher Anita Tseng.
Intel ISEF is the premiere international science competition for high school students. It grew out of the National Science Fair, which was created by Society for Science & the Public (then known as Science Service) in 1950. In 1958, the fair became international for the first time when Japan, Canada, and Germany joined the competition.