The value of pi

[vasantha syamalam]

Please give the meaning of this shloka.

गोपी भाग्य मधुव्रात् शृङ्गीशो दधिसन्धिग्।

खलजीवति खाताव गलहालारसन्धर॥         

                                                -भारतीतीर्थः

 We can find out the value of  pi  with the help of this shloka, but what is the meaning of this shloka?

Vasantha syamalam

[Mrugesh]

You can find more details here.. 

http://en.wikipedia.org/wiki/Katapayadi_system

described how the above verse is derived.. 

Regards

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सस्नेहं,

Mrugesh मृगेशः
Cell: 408-835-8394

[Shreevatsa R]

See the earlier thread at https://groups.google.com/forum/#!msg/samskrita/pWNFDE7apiw/9TxRj68-gv0J

This shloka was composed by (as far as one can tell) Swami Bharati Krishna Tirtha and published in his 1965 book "Vedic Mathematics", but he seems to have taken some liberty with meaning to make it fit the digits (or to say it differently, it requires quite an effort of interpretation on the part of the reader).

[Hnbhat B.R.]

This was once discussed in this forum earlier long ago:

https://groups.google.com/d/msg/samskrita/pWNFDE7apiw/PqpLP9G9aO4J

But no one could give the correct word by word translation for the verse, or meaning in two ways, applicable to Krishna and Shiva in addition.

[KN.Ramesh]

I got this :

gopi bhagya madhuvrata
srngiso dadhi sandhiga
khala jivita khatava
gala hala rasandara

The translation is as follows:

O Lord anointed with the yogurt of the milkmaids’ worship (Krishna), O savior of the fallen, O master of Shiva, please protect me.

from here:

https://hindufocus.wordpress.com/2009/07/16/the-sanskrit-verse-for-the-value-of-pi/

[Arvind_Kolhatkar]

Aryabhata I had given the following value of 'pi' in Aryabhatiya.

व्यासे भनन्दाग्निहते विभक्ते

खबाणसूर्यै: परिधिः सुसूक्ष्मः।

द्वाविंशतिघ्ने विहृतेऽथ शैलै:

स्थूलोऽथवा स्याद्व्यवहारयोग्य:॥

Diameter multiplied by भ (27), नन्द (9) अग्नि (3) i.e. by 3927 and divided by ख (0), बाण (5), सूर्य (12)  i.e. by 1250 yields the relatively exact value of the circumference.  (In other words, if the diameter is taken equal 1 unit of length, the circumference will be 3927/1250 units of length.) Diameter multiplied by 22 and divided by 7 (there are 7 शैलs or कुलपर्वतs), the result is a broad one, suitable for day-to-day use.

Hindu mathematicians generally regarded 'pi' in broad measure to be equal to the square-root of 10.

The Kerala mathematicians of the 13-14 centuries had further refined to value of 'pi' by use of the technique of summation of infinite series.  A British official, Charles M.Whish, who was interested in the Kerala Mathematics had published a paper on this in a meeting of the Madras Literary Society on December 15, 1832.  Internet has a lot of info on Whish, his paper and the Kerala school of Mathematics.

Incidentally, the nomenclature 'pi' to denote the transcendental number representing the ratio between the diameter and circumference of a circle was first used by in 1706 by William Jones, a British Mathematician, who was the father of the orientalist Wilson Jones of Calcutta.

Arvind Kolhatkar, Toronto, December 17, 2014.