A Sanskrit Mnemonic for π

In ancient India, a system called Bhūtasaṃkhyā used Sanskrit words to denote numbers. Words that had a connotation of numeric values were used together to form phrases that helped record and remember large numbers. For example, the word ‘eye’ can be associated with 2, and ‘tooth’ with 32. A prominent Indian mathematician of the late fourteenth century from Kerala – Mādhava – used this system to come up with this amazing little Sanskrit verse that contains a numerical approximation for π:

Gods, eyes, elephants, serpents, fires, three, qualities, Vedas, nakshatras, elephants, arms: the wise man have said that this is the measure of the circumference when the diameter of the circle is nine nikharvas.

There are 33 crore devas (gods), 2 eyes, 8 elephants, 8 serpents, 3 kinds of ritual fires,  3 gunas (qualities), 4 Vedas, 27 nakshatras,  and 2 arms. If we arrange these numbers from left to right (in increasing order of their place value) we get the following number: 2,827,433,388,233.

Now one nikharva is equal to 100,000,000,000. And the diameter of the given circle is nine nikharva. If we divide the circumference by the diameter, we should get the value of π.

This equation gives the correct value of up to the first 11 decimal points! Pretty cool, eh?



Here’s the Wikipedia page on Bhūtasaṃkhyā System. And the source of this wonderful verse is Mathematics in India.


3 responses to “A Sanskrit Mnemonic for π

  1. DW

    Could you give us the Sanskrit?

    • I found the original Sanskrit shloka (verse) on Wikipedia. See below (last two lines):

      I have a very very limited knowledge of Sanskrit so I can’t say for sure – but the following transliteration seems to be accurate:

      nava-nikharva-mitē vr̥tivistarē
      paridhi-mānamidaṁ jagadur̥ budhāḥ

      Gods (vibudha : 33), eyes (nētra : 2), elephants (gaja : 8), snakes (ahi : 8), fires (hutāśana : 3), three (tri : 3), qualities (guṇa : 3), vedas (vēda : 4), naksatras (bha : 27), elephants (vāraṇa : 8), and arms (bāhavaḥ : 2)


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