Kolam – Artwork of India

Rotational Symmetry Updated Fall 2012

Tamil Threshold Designs

Flour in right hand, women drop flour/stone to make a curve through thumb and pointer finger.

“The Indian ritual of creating rice Kolam at the start of each day has been passed on from mother to daughter for thousands of years.”

.…

…..…….…..….

The pattern normally starts with putting the dots as follows:

Women make a curve around the dots.

Kolam Example #1

http://www.tamilnation.org/images/culture/kolam/kolam5.jpg

Kolam Example #1

Rotational symmetry at 90, 180, and 270. Smallest angle of rotation is shown. (picture taken slightly off center)

Kolam Example #2

http://www.kamat.com/kalranga/tnadu/4103.htm

Kolam Example #2

Reflection symmetry: horizontal, vertical, and 2 diagonal lines of symmetry

Kolam Example #2

Rotational symmetry at 90, 180, 270. Smallest angle of turn sym shown.

Kolam Example #3

http://www.blueavatar.com/Kolam/Designs/ImageSelector.php

How many lines of symmetry does this design have? A) 0 B) 1 C) 2 D) 3 E) 4

http://www.blueavatar.com/Kolam/Designs/ImageSelector.php

Kolam Example #3

No lines of symmetry, but Rotational symmetry at 90, 180, 270

Kolam Example #4

http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

What is the smallest angle of turn symmetry? Assume light and dark blue are to be treated as the “same color tone”. A) 30 B) 45 C) 60 D) 108 E) 120

http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

Kolam Example #4

Rotational symmetry at 60, 120, 180, 240, 300

So smallest angle is 60 degrees (blues as same).

Kolam Example #4

Six lines of reflection symmetry: horizontal, vertical, and diagonal line symmetry

Polygon Behind #5Regular Hexagon

The angle of this photo affects the viewing of the regular hexagon.

http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

Kolam #5 - if dark blue is matched to dark blue, the symmetry changes

http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

Kolam #5 - if dark blue is matched to dark blue, the symmetry changes

Now based on the symmetry of a regular triangle

angles of turn symmetry are multiples of 120 degrees

http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

Kolam #5 - if dark blue is matched to dark blue, the symmetry changes

Now smallest angle of turn symmetry is 120 degrees as shown above.

http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

Kolam #5 - if dark blue is matched to dark blue, the symmetry changes

Now 3 lines of reflection symmetry as shown.

http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

Kolam #5 - if dark blue is matched to dark blue, the symmetry changes

Now 3 lines of reflection symmetry as shown inside regular triangle.

Going through vertex to midpoint of opposite side.

http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

Summary/Conclusion

Rotational symmetry seems to exist in about 90% of the designs, while reflection symmetry only in about 25%

Usually the designs are curved lines and no well known math shape is made directly in the design.

Behind the scenes regular polygons with an even number of sides drive the symmetry of the design.

Summary/Conclusion

Two types of images that did appear in several designs were flowers and birds

Due to the use of powdered stone or chalk, usually the design is white in color

References

Images and Background Information:

http://www.tamilnation.org/images/culture/kolam/kolam5.jpg

http://www.kamat.com/kalranga/tnadu/4103.htm

http://www.saigan.com/heritage/alangaram/kolams/pko4.html

http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

http://www.blueavatar.com/Kolam/Designs/ImageSelector.php