Kolams and Symmetries of Border Patterns

This student chose a simpler motif. Here, they have repeatedly rotated their motif 180 degrees, using both positive and negative space to create visual interest from a simple arrangement.

A student at Ogden International learning about kolams, were art and math meet.

A student at Ogden International learning about kolams, were art and math meet.

 

 

Looking back over 2017, Eye on India is still smiling from its great experiences with two Chicago public schools. In the spring, Eye on India was back in the fourth-grade classrooms of Ogden International School with Dr. Sunita Vatuk. The workshops focused on exposing students to the South Indian tradition of kolam. The students practiced their observation skills and related those observations to mathematics in what was, for them, an unexpected context. You may visit Eye on India’s blog posts for more information on the beautiful tradition of kolam making: http://eyeonindia.org/blog/taxonomy-delight-observer/ and http://eyeonindia.org/blog/cps-kolam-workshop-sunita-vatuk/

Dr. Vatuk then teamed up with artist and EOI Visual Arts Director Tanya Gill at the Chicago High School for the Arts – known as Chi-Arts – for a workshop created especially for the freshman course Drawing by Design taught by Kayce Bayer. That workshop opened students’ eyes to mathematical structures in design, this time focusing on the language and mathematics of symmetry.

The fact that there are only seven possible combinations of symmetrical border (or frieze) patterns is well-known to students of mathematics. However, this fact is not familiar to most artists and designers. In this workshop, Vatuk and Gill used what seemed at first to be a limitation to spur creativity.

Starting with a slide show of frieze patterns found in Indian architecture, art, and textiles, the workshop shifted between making designs, analyzing designs, and then using the analysis to find new possibilities.

Math is often thought of as a purely mental activity, however Vatuk was promoting the idea that when studying symmetry, it is important to engage the body as well. The physical act of rotating the paper cut-outs to make a design with rotational symmetry, or turning the paper motif over to make a design with a reflection symmetry is more powerful than just looking.

This student figured out that choosing the symmetries does not put an end to trying different ideas. Here they have used the same motif and the same symmetries (180-degree rotation and translation) to create two designs with very different impact.

This student figured out that choosing the symmetries does not put an end to trying different ideas. Here they have used the same motif and the same symmetries (180-degree rotation and translation) to create two designs with very different impact.

 

The key to being able to explore all possible combinations of symmetries was to start with a motif that had no symmetry of its own. A student holds up their proposed motif for inspection.

The key to being able to explore all possible combinations of symmetries was to start with a motif that had no symmetry of its own. A student holds up their proposed motif for inspection.

 

This student chose a simpler motif. Here, they have repeatedly rotated their motif 180 degrees, using both positive and negative space to create visual interest from a simple arrangement.

This student chose a simpler motif. Here, they have repeatedly rotated their motif 180 degrees, using both positive and negative space to create visual interest from a simple arrangement.

 

 

 

 

 

 

 

 

 

 

 

 

 

Vatuk and Gill were very impressed with the students’ technical abilities and visual sensibilities; the high school freshman class had the atmosphere of a first-year college studio.

 

Eye on India is in the unique position of being able to offer these artistic and academic workshops that encompass art fundamentals, mathematics, and Indian Culture. It is exciting to be in the position to offer students an educational experience that demonstrates life’s ‘interconnectedness’ as well as its diversity. Planning is underway to offer similar workshops in the spring of 2018, cementing Eye on India’s dedication to Chicago’s youth.

Students glue down one or two choices of pattern using the paper cutouts, and then analyze the symmetries in each other’s designs with Dr. Vatuk’s help.

Students glue down one or two choices of pattern using the paper cutouts, and then analyze the symmetries in each other’s designs with Dr. Vatuk’s help.

 

Gill talking about the negative and positive elements of the pattern.

Gill talking about the negative and positive elements of the pattern.

 

 

 

 

 

 

 

 

 

 

 

 

 

* The first image shows part two of the process, making your shape into a stamp. Once students had the stamps, they could more quickly try out different symmetries. However, with only one stamp, students could only use translation and rotational symmetries – reflections require a second stamp. Vatuk and Gill wanted the students to figure that out for themselves.

 

 

 

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Eye on India is a young and dynamic organization whose role is to serve as a facilitator and integrator. Promoting appreciation for diverse programming in the cultural landscape of Chicago, the festival’s uniqueness lies in its ability to create and inspire collaboration among various cultural, community and business organizations across Chicago and other cities in the US and India.

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