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The earliest known examples date from the seventeenth-century. Meditation and worship focused upon the contemplation of intricate geometrical objects, the most
elaborate of which is the Sri yantra, or 'supreme object', which is a member of a large class of yantras ('objects') used for meditational and ritual purposes.
It consists of a fourteen-sided polygon at the centre surrounded by eight- and sixteen-petalled lotus flowers surrounded by three circles before an outer
boundary containing four 'doors' leads to the outside world. The central pattern consists of forty-three small triangles, where the gods reside, is produced by the precise intersection of nine
large triangles. Of the nine central triangles, four pointupwards marking 'male' cosmic energy, and five point downwards marking 'female' enrgy. Very precise geometrical knowledge and draughtsmanship
is required in order to achieve the intersections of more than two lines at single points. This structure was used for meditation in two ways. Either, beginning from bhupura, the outside realm of
disorder, proceeding through the doors, into the realm of the gods, past the three circles to the central point, or bindu; or outwards from the central point to the bhupura. The outward path is taken to
represent the path by which the Universe evolved from nothingness and static harmony into greater diversity and complexity and is characteristic of one Tantric sect, The other path from the outside inwards,
represented the gradual dissolution of the Universe.
Remarkably, Sri yantra exist with curved hemispherical surfaces on which the intersections and points have been constructed using (what in the West was called)
non-Euclidean geometry.
Further reading:
Barrow, J.D. Pi in the Sky, Oxford UP (1992).
Bolton, N. J. and Macleod, D. N., The Geometry of Sriyantra, Religion 7, 66 (1977).
Kulaichev, A. P., Sriyantra and its Mathematical Properties, Indian J. Hist. Sci. 19, 279 (1984).
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