Connecting the Dots- Math and Kolam (Rangoli)

Walk on any street in Tamil Nadu or most places in Southern India and you will find beautiful designs on the street outside every house. You will find women sweeping their courtyards early in the morning and drawing these beautiful designs. These designs are called kolam or rangoli. Kolam or Rangoli are traditional line drawings that are usually drawn outside a house or in front of the puja room. It is considered auspicious and is drawn everyday. On special occasions, like festivals or an important event in the house, the drawings are elaborate and more colorful. Rangolis are usually drawn using finely ground rice flour, chalk powder or chalk.

When I was growing up in Bangalore (Bengaluru), there were hardly any apartments. (I had seen pictures of apartments in Mumbai or NY, but not in Bangalore.) Every morning, usually the woman of the house, cleans the entrance and then draws a Kolam/ Rangoli in front of the house. My mother does it even today. Many moons ago, Bangalore was a small town, where everybody knew their neighbors. We exchanged homemade sweets with our neighbors on festivals and gossiped during power cuts when everybody came out to the verandas or porches (these were days before generators and UPS). People came out and admired the other person’s rangoli and had conversations. Those were simple times. Today, Bangalore is full of apartments and most people do not have time for rangolis every morning. You get stickers which you can stick on the floor and you see that in some apartments. On festivals and holidays, you may find women coming out to draw rangolis.

But even today you find rangolis in small towns and villages. During Pongal, the harvest festival in Tamil Nadu, you find huge colourful rangolis, each trying to outdo the next. During Onam, in Kerala, pookolams are drawn and decorated with flowers.  It is said that kolams and rangolis use rice flour as an offering/food to ants, bugs and birds. Here is a picture of a kolam made at home for a religious function.

Here are some pictures of Rangolis that my friend Bhagya drew in front of her house for various occasions.

As a kid, I was always enamored by the designs and remember buying small rangoli books and practicing rangolis on paper. When I moved to the US, I taught children including my own to draw rangolis.

Recently, I saw an Instagram post which had new designs every day. This ignited my interest to draw rangolis again. I started reading more on rangolis and math and started reading articles on them. Here are some of my attempts at drawing rangolis.

When I became a teacher, I started looking at rangolis in a new light. They were not just designs or patterns any more. Could we use it to teach math? I remember teaching arrays in Grade 4 co-teaching with other colleagues. Kalpana, one of my former colleague, is an amazing artist. We always looked to her for ideas to bring art while teaching math. She would introduce simple rangolis to students and they would use arrays to draw their rangolis. We would give them dotted sheets for this. Here is an example of what you can do with arrays; other than teaching them just multiplication and division with it.

A fun activity to do with kids when teaching arrays. A 5×5 array is 25. The sum of first 5 odd numbers(1+3+5+7+9) is 25 . A 3×3 array is 9. The sum of first three odd numbers is 9. Get kids to draw different arrays and see if it works. This only works for square arrays (n xn). Not only do they have fun, they learn to add, multiply and learn about odd numbers. Kids love these activities. Try it with them.

As I started looking up and reading more, I started thinking beyond symmetry and rangolis. Symmetry can be taught from 1st grade all the way to higher classes differentiating the level of teaching. To start with a first grader one would teach mirror symmetry or reflection symmetry. In later years, one would teach rotational and point symmetry and lines of symmetry. Most kolams/ rangolis have symmetry. The symmetry has recurring fractals (never ending pattern). Check out the rangolis to look for different types of symmetry and lines of symmetry.

As a kid, we were all asked to draw a house without lifting your pencil; do you remember that? I remember trying to draw different designs and having challenges with friends. I remember asking my kids the same question. This is Euler’s cycle.

There are many scientific papers and books written about rangoli and math. Here are some if you are interested:

https://feedingathousandsouls.com/

https://www.researchgate.net/publication/323182804_The_Mathematical_Aspects_in_Art_to_Create_Decorative_Effect_in_Design_Patterns

Kolam/Rangolis are evolving from the traditional designs to newer designs. Many years ago when we were visiting Pondicherry, there was a rangoli competition on the beach front. The promenade was filled with rangolis. Here are some pictures. Enjoy!

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