Mathematics

Number tricks are fun to perform and are an excellent way to enhance mathematical skills. When I was young, we used to discuss a lot of number tricks. One amongst those was as follows:

Take a number with a lot of digits. For example, suppose you think of 2134567. Add its digits: 2 + 1 + 3 + 4 + 5 + 6 + 7 = 28. Subtract 28 from the original number taken, 2134567. You’ll get some answer, say abcdefg.

We live in an era of data and information. Right from deciding what to read, what to wear, which restaurant to go to, which city to visit, whom to vote for, we consider ourselves rational human beings who rely on data to make all our decisions. How much of this data is based on facts rather than opinions and/or perceptions? This review looks at two websites, Gapminder and Our World in Data, which attempt to provide reliable global statistics and promote a fact-based worldview.

In this edition of ‘Adventures’ we study a few miscellaneous problems.

A question about angle bisectors Consider a △ABC in which D, E and F are the midpoints of the sides BC, CA and AB respectively. Let G be the centroid of triangle ABC, i.e., the point of intersection of the medians AD, BE and CF. It is well-known that G is also the centroid of triangle DEF. If, instead of being the midpoints, the points D, E and F are the points of intersection of the internal bisectors of