Kolam figures and it's connection to mathematical ideas

Drawing Kolam is a very important tradition followed by women in the state of Tamil Nadu in India. Women from different educational backgrounds follow this tradition, and they teach girls the types of Kolam and how to do Kolam figures to keep up the tradition in their culture. There are similar traditions outside Tamil Nadu that practices drawing patterns on the floor which includes Rangoli, Muggu and Alpana. Each type of figures differ as the pattern and their meanings differ from each other. 

According to Ascher (2002), in the recent decades the tradition has attracted the interest of computer scientists in analysing and describing the patterns, and has found that the Kolam tradition has contributed to the modern computer science in several ways. 

In this article, we will be looking into the connection of Kolam figures to mathematical ideas. The Kolam is drawn by following continuous curves which are drawn symmetrically around horizontal lines, vertical lines, dots or several kinds of rotational symmetry. 

In reference from Ascher (2002), it can be noted that Kolam has an algorithmic nature to it, where the women use step by step techniques to finish the figure. There is a rich contribution of symmetry, patterned repetition, families of curves and continuous curves in each figure. 

According to Yanagisawa et al., (2007), there are certain rules that needs to be followed while drawing the Kolam figure. All the rules are related to mathematics, whether it is the pattern, symmetry, structure, arcs or angles, to complete the Kolam everyone should follow certain rules. Every family develops their own rules to complete their particular pattern, but in common some of the rules are as below:

1. Loop drawing-lines, and never trace a line through the same route.
2. The drawing is completed when all points are enclosed by a drawing-line.
3. Straight lines are drawn along the dual grid inclined at an angle of 45°.
4. Arcs are drawn surrounding the points.
5. Smooth drawing-lines. Lines should not bend in a right angle.

(Yanagisawa et al., 2007)

Picture from: Nirmisu (2020)

References:

1. Ascher, M. (2002). The Kolam Tradition: A tradition of figure-drawing in southern India expresses mathematical ideas and has attracted the attention of computer science. American Scientist, 90(1), 56–63. http://www.jstor.org/stable/27857597
2. Yanagisawa, Kiwamu & Nagata, Shojiro. (2007). Fundamental Study on Design System of Kolam Pattern. 
3. Nirmisu (2020). Kolam — The floor art and its types [Intricate designs of the Sikku Kolam]. Medium. https://medium.com/@nirmisunirmisu/kolam-the-floor-art-and-its-types-94edcad0f9a5