Some geometric inspiration from India

yantra and rangoli
Sri Yantra

It’s nearing monsoon and Dataisnature returns to the seam after a few months in hibernation. Some inspirations from my travels in India.

The Yantra:

The Yantra is meditation diagram or ‘psychocosmogram’ containing linear and spatial geometrical permutations of the polarity between Shiva and Shakti. The form consists of the dot (or bindu – the mathematical point of zero dimension) and sets of mathematically defined interlocking triangles (upright for the male and inverted for the female) that are contained in a lotus circle as part of a larger diagram – the Mandala. ‘Yantra literally means loom, instrument or machine.

Yantras are found all over India, in temples and homes and within the contexts of worship and meditation. I was interested in the geometry of the Yantra, particularly the difficult to draw interlocking triangles, and wondered if there is prescribed way of making these symbols or a set of mathematical instructions?

What little info I could find mentioned instinctual methods of drawing these symbols, the result of practice and reference to a ‘mathematical’ meditation. A little browsing and I found this page, which gives very precise instructions, measurements and ratios for producing the sigil using a protractor, compass, pencil, and ruler. The page is also interesting in that it explains what some of the number ratios within the diagram represent in mythological terms.

Another page concerning the construction of the Sri Yantra, also containing pictures of beautiful three-dimensional yantras.
Images of Yantras

Added 27|03|07 : Mikel sent me a link to his research on the maths of the Sri Yantra plus other interesting findings.

Rangolis (also know as Kolams):

Rangolis, mentioned before at Dataisnature, are geometric drawings produced procedurally by joining up, or interweaving within, a skeletal matrix of dots (resembling a knitting pattern). These drawings are made by women early in the morning using chalk dust on wet earth. Hampi, built on the ruined city of Vijayanagar, seems to be the hotspot for seeing Rangolis in Southern India, not since the town awakes at 5am each morning – your early morning alarm call for a roam around the village to see these curious patterns being run in real time. Here’s a Flickr set containing my photographs of Rangolis in Hampi.

Rangolis are sign of invitation into the home, as well a symbol to prevent evil spirits from entering. They are also used to commemorate special occasions such as births or weddings, ‘When people get married, the ritual Kolam patterns created for the occasion can stretch all the way down the street. Patterns are often passed on generation to generation, mother to daughter.’ – wikipedia

Thanks to all those who sent mail while I was away, apologies if I could not reply while distant from wires (I’ll be processing them all shortly). And not so much thanks to the all the spam I received that made any response to comments on posts impossible. I had to go in and delete over 10,000 comments. Robots win! It’s likely that robots will take over the world in a more insidious way then previously imagined….

Anyway, comments are now switched back on and if you did post a comment in the last 4 months id be very grateful if you could do so again.

6 Responses to “Some geometric inspiration from India”

  1. Mikel Maron writes:

    I did a lot of research years ago into the mathematics of Sri Yantra construction ..

  2. rand writes:

    welcome back

  3. paul writes:

    thanks mikel, nice resource there! particularly enjoyed ‘A note on Computational Complexity of Sri Yantra’ by Kulaichev

  4. paul writes:

    thanks rand!

  5. Pravin Patel writes:

    Hi Mikel,
    I can’t access articles at

    Did web page location moved ? Can you email me new location.


  6. vneus john writes:

    thanks,i am going to try and draw the sriyantra..I think it will improve my mind..

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