Abstract:
We all know that 1/3 = 0.3333… and 1/(3x3) = 0.1111… have the same number of digits - one - in their recurring parts. (Is 3 the only prime with this property in base-10?) More generally, one can ask how many digits 1/d has in its recurring “decimal” expansion, in base 10 or any other base. We will see the answer to this question. If time permits, we will see a century-old conjecture of Emil Artin, that holds for at least two bases among 2, 3, 5, 7 - but even today we don't know which!
About the Speaker:
Apoorva Khare is an Associate Professor of Mathematics at the Indian Institute of Science (IISc), Bengaluru. After his B.Stat. from ISI Kolkata and MS+PhD from University of Chicago, he worked at UC Riverside, Yale, and Stanford before returning to India and joining IISc. Apoorva is a Ramanujan and SwarnaJayanti Fellow of SERB and DST, a Fellow of the Indian Academy of Sciences, and a recipient of the Shanti Swarup Bhatnagar Prize and Ganit Ratna Puraskar. Apart from many papers, he has written two Maths books, including one on real-world non-calculus non-trig mathematics, that arose from a course he introduced at Yale.
Eligibility:
Students in grades 9 through 12 with a keen interest in mathematics.
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