You can get an impression of kolams and sona by watching the first two Youtube videos in the link list below. Kolams and sona are the subject of ethnomathematics. There are links at the end of this web page. Example of a kolam, example of a lusona
In other regions, point grids and lines are dispensed with. Instead, coloured areas or carpets of flowers are laid out. Rice flour is replaced by stone powder or chalk powder, often together with natural or synthetic colour powders. The pictures, which always have rotational symmetry, are presented together with the stroke kolams at celebrations, at festivals, in competitions and on the internet. Simple Example
Example of a Kolam This kolam is created by seven closed curves, marked by the lines in red (4x), green, blue and violet. The structure of the kolam is better recognized by yellow colorings. - There are four outer figures and a central circle. - In the center is a rounded cross. - A square with tines surrounds the figure.
Several closed lines, this is typical for kolams, although they sometimes get by with one closed line.
Simple Example The figure to a 4x3 grid is a lusona. It therefore consists of a closed line without beginning and end. The figure is monolineal.
As the sona complement stories, they often depict animals. Antelope
Leopard
Three Birds
A Fable
Exceptionally, when the story requires it, sona consists of several closed lines. But on this page, for simplicity, a figure is called a lusona when they arise from a closed line.
First Rule The question arises which rectangular figures m*n is a lusona. Here are four examples: ... ... These four examples illustrate the following first rule.
- A closed line only results if m and n have no common divisor. - If several closed lines are necessary to create the figure, the number of curves is equal to the greatest common divisor. The rectangles to the leopard family have the data 10*3 and 2x3, their dimension numbers have no common divisor.
Inner two-sided mirrors
With the insertion of a mirror, the following figure can no longer created by a closed line.
Second rule There is a simple rule for m*n-sona with one interior mirror. For this, a pattern of dark and light fields must be introduced.
Another example, the 5*4-Lusona ... From a Lusona to a Matrix
Question: In the 3x3 kolam, where must the double mirrors (blue) be inside and on the edge for the figure to become a lusona? ... Result: There are 36 sonas, nine of which are symmetrical. ... Question: How do you get to the following kolam of five closed curves? ...
Just like the mandalas of Far Eastern cultures, the line kolams lend themselves to their own activities. Drawing with pen and paper For example, if you have a 3x2 dot pattern and want to draw Kolams or even Sona, this is the best way to go. - Draw a 3x2 rectangle and double mirrors at suitable places. - Then you sketch the kolams. It is difficult to do this, because you have to have the five basic figures in your head. - Then the sketches are transferred into a final drawing. Use MS-Paint or the online program described below. ... Drawing with MS-Paint The drawings on this website were created with the drawing program MS-Paint. It is available to anyone who uses Windows on the Internet.
I show two sequences of pictures as a suggestion for your own activities. ... You can color the kolams. ... Drawing with a program There is a program available on the Internet that makes it easy to draw kolams. You can get to the online program by calling it in the link list below with the name Forkphorus. The user interface is clear. On the right is the tool, on the left is the drawing area for a maximum of 5x5 Kolams. At the top the six basic figures are available. You can bring a figure to the drawing area by tapping on it and then on the target square. There are fields for turning and deleting the figure. The field at the bottom right deletes the drawing. The field at the bottom left has no effect on me. The program helped to find the sona among the 3x3 kolams in the previous chapter. If you specify the compact 3x3 figure, you can "create" kolams by turning basic figures. You can recognizes the position of the double mirrors as gaps and can make out sona, even if the shapes are not correct. Suggestion Perhaps an open question is how many kolams and then sona there are to the compact, relatively simple 3x2 and 4x2 rectangles. So for this, you have to look for the possible positions of the double mirrors with the help of notes on squared paper systematically. In a second step, you can recognize the sona with the help of the online program. Kolam Game If you glue the basic figures on squares of cardboard, you get a game to lay. ...
Celtic knots The 3x3-Kolam and the 4x3-Lusona become Celtic knots, if you make the lines thicker and place along a line alternating underpasses and bridges.
Indian Sand Painting
German Beach Painting :-)
Knight's Tour
German Alban Da Silva (Spektrum)
arte.tv
Henning Krause (Spektrum) Dr. Henning Krause (Spektrum) Ethnomathematik - dargestellt am Beispiel der Sona Geometrie Labbé pulli-kolams, Was sind Sona? M. Weber, A. Mischau (Mathematisches Panorama) Mathematik und (bzw. in) andere(n) Kulturtechniken (.pdf-Datei) Wikipedia Kolam, Sona (Mathematik), Paulus Gerdes, Ethnomathematik , Sandbild, Sandanimation English Darrah Chavey
Darrah Chavey Constructing Symmetric Chokwe Sand Drawings Forkphorus Drawing program Ljiljana Radovic MIRROR CURVES Marcia Ascher (spektrum.de) Ethnomathematik: Die Kolam-Figuren Südindiens Mattia De’ Michieli Vitturi Sona drawings, mirror curves and pattern designs NN Sona - Sand Drawings from Africa Paulus Gerdes m-Canonic mirror curves Paulus Gerdes Geometria Sona de Angola Matemática duma Tradição Africana Portuguese, 191 pages, lots of illustrations Slavik Jablan, Ljiljana Radovi, Radmila Sazdanovi Ana Zekovi Knots in Art South African History Online Sona Patterns - Revisiting the Contributions of the People in Sub-Saharan Africa to Modern Mathematics Wikipedia Kolam, Rangoli, Lusona, Sandpainting, Sand animation, Sand mandala, Ethnomathematics, Zenigata Sunae Youtube Angolan Sand Drawings Some drawings and stories Youtube CHIKKU KOLAM WITH 10-2 DOTS | HOW TO DRAW A SIKKU KOLAM | NELI KOLAM Example of an Indian floor painting Youtube Pongal' theme for Chennai's Kolam and Rangoli competition A meeting of women artists Youtube Kolam designs Collection of videos
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