Kolam – Artwork of India

1. Kolam – Artwork of India Rotational Symmetry Updated Fall 2012

2. 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.”

3. The pattern normally starts with putting the dots as follows: . … ….. ……. ….. … . Women make a curve around the dots.

4. Kolam Example #1 http://www.tamilnation.org/images/culture/kolam/kolam5.jpg

5. Kolam Example #1 Rotational symmetry at 90, 180, and 270. Smallest angle of rotation is shown. (picture taken slightly off center)

6. Kolam Example #2 http://www.kamat.com/kalranga/tnadu/4103.htm

7. Kolam Example #2 Reflection symmetry: horizontal, vertical, and 2 diagonal lines of symmetry

8. Kolam Example #2 Rotational symmetry at 90, 180, 270. Smallest angle of turn sym shown.

9. Kolam Example #3 http://www.blueavatar.com/Kolam/Designs/ImageSelector.php

10. 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

11. Kolam Example #3 No lines of symmetry, but Rotational symmetry at 90, 180, 270

12. Kolam Example #4 http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

13. 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

14. Kolam Example #4 Rotational symmetry at 60, 120, 180, 240, 300 So smallest angle is 60 degrees (blues as same).

15. Kolam Example #4 Six lines of reflection symmetry: horizontal, vertical, and diagonal line symmetry

16. Polygon Behind #5 Regular Hexagon The angle of this photo affects the viewing of the regular hexagon. http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

17. Kolam #5 - if dark blue is matched to dark blue, the symmetry changes http://pudukkottai.org/archieve/pongal-2003/images/DSCN0046.jpg

18. 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

19. 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

20. 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

21. 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

22. 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.

23. 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

24. 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