Predicting the future

VISWANATH, SANKARAN (2017) Predicting the future. At Right Angles, 6 (2).

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Abstract

W e often find ourselves needing to predict the future value of something based on past trends. For instance, climate scientists have been trying to estimate the future rise in ocean temperatures based on (among other things) temperature data of the last 100 or more years. Or maybe you are a cricket enthusiast and want to predict how many centuries your favourite batsman will score this year based on his scoring statistics for past years. We all probably have our own ways of arriving at an estimate! In this article, let us explore one approach. 1 Tweedledum and Tweedledee appear in Lewis Carroll’s Through the Looking Glass. Carroll, whose real name was Charles Lutwidge Dodgson, was (among other things) a mathematician who taught at Oxford. The poem above is inspired by Carroll’s literary nonsense style which is the hallmark of the Alice books. Keywords: Patterns, polynomials, extrapolation, interpolation At At Right Right Angles Angles | Vol. 6, No. 2, August 2017 PB 15First, imagine this: you are growing a bacterial culture in the lab, and would like to understand how the population of bacteria changes over time. So, at the end of every hour you measure the bacterial population, and write down the sequence of measurements as follows: a 1 , a 2 , a 3 , . . . , where a n denotes the population after n hours. Now, suppose you find that the first five measurements are: 1 , 4 , 9 , 16 , 25. Can you “predict” the population after 6 hours? You probably guessed 36, right? If asked why you think this a good estimate, you would probably say “the pattern of the previous measurements suggests that the population is varying as the square of the natural numbers, i.e., 1 2 , 2 2 , 3 2 , . . . ; so at the end of 6 hours, it must be 6 2 = 36.”

Item Type: Articles in APF Magazines
Uncontrolled Keywords: Patterns, polynomials, extrapolation, interpolation
Subjects: Natural Sciences
Natural Sciences > Mathematics
Divisions: Azim Premji University > University publications > At Right Angles
Depositing User: Mr. Sachin Tirlapur
Date Deposited: 15 Sep 2018 10:01
Last Modified: 15 Sep 2018 10:01
URI: http://publications.azimpremjifoundation.org/id/eprint/1339
Publisher URL: http://apfstatic.s3.ap-south-1.amazonaws.com/s3fs-...

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