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.”
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…..…….…..….
The pattern normally starts with putting the dots as follows:
Women make a curve around the dots.
Kolam Example #1
Rotational symmetry at 90, 180, and 270. Smallest angle of rotation is shown. (picture taken slightly off center)
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
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).
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
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