Folk Mathematics

In this book we have been exploring the development of mathematics by understanding the lives of mathematicians and their work. But the knowledge of mathematics did not stay only with mathematicians. It also permeated the culture, language & commercial lives for the common folk. We can call the math that was prevalent among the common folk as Folk Mathematics. Folk mathematics is mainly about ordinary folks using mathematics for entertainment.

This is because the starting point of math was numbers & shapes in the patterns around us. Common people also observed these and internalized them in their own way. It is possible that the specialized profession of a “mathematician” came into being only after the prosperity & possessions of the agricultural revolution, which is about 10,000 years old.

Many events were possibly taken up for study by mathematicians only after the folk had already absorbed it in their lives. The bridges of Konigsburg is one such example.

Folk mathematics developed in all areas where societies developed. It grew into vast traditions of number language, songs, jokes, puzzles, games. If these folk mathematical traditions are not documented, they may just disappear from our common memory.

Let us see a few examples.

Art – Kolam & Rangoli are obviously based on math, symmetry and aesthetics. Even today many women can effortlessly draw a complicated pattern with dots & lines on the floor just by practice & intuition. Hindu religious rituals require the drawing of yantras which are geometrical drawings.

Games – Tic-Tac-Toe, Chaturanga (chess), Pachisi (Ludo), Parama pada (Snakes & Ladders) and Pallanguzhi, Go and Nim were all games based on math principles. Any person who could understand the mathematics of the game could win easily. Sakuni in the Mahabharata must have been one such expert.

Gambling – Many of the above games are competitive and hence can be adapted for wagering and gambling.

Puzzles – Each culture has many collections of puzzles which are based on math. The farmer wanting to divide 17 horses among his 3 sons in the ratio ½, 1/3 and 1/9 is prevalent in many cultures in many forms. Many stories of King Vikramaditya & the Vetal are based on puzzles.

Magic Squares – Making magic squares of various sizes was also a popular pastime, with many of them carved in stone. The traditional Hindu almanac or Panchang has magic squares in it.

Jokes – Math was always a difficult subject for many who do not understand the concepts very well. Hence there are many jokes which use the misunderstandings of and about math.

Approximations or back-of-the-envelope calculations – People have difficulty is calculations which involve complex calculations. There are simple approximations to estimate the results of such complex calculations.

A recent Whatsapp thread provided one such approximation of the hypotenuse of a right-angled triangle by a Tamil Siddha called Bodaiyanar. It was for calculating the distance one had to travel to a hill temple, if the distance to the hill and the height of the hill were known. The formula, given as a couplet, comes out as 7a/8 + b/2 where a is the distance to the hill and b is the height of the hill. The result is remarkably exact if a & b were in the ratio 3:4 or 5:12. This approximation would have required an understanding of the Pythagoras theorem.

The rest of this section has articles on various forms of entertainment using math.