Previously, we saw the nihatya series for jyā and śara and how that enables a very accurate estimate of those functions for any arc, accurate to the fourths. We also saw how this led to the partially precomputed vidvān series as well as the table of पठितज्या accurate to thirds – श्रेष्ठं नाम वरिष्ठानाम् etc. …
Monthly Archives: June 2021
A Better Bowstring: The Mādhava Jyā Series
What’s better than an improved jyā table and an improved method for interpolation? A full jyā series that lets you compute jyā of any arc, to any degree of precision you wish. निहत्य चापवर्गेण चापं तत्तत्फलानि च । हरेत् समूलयुग्वर्गैस्त्रिज्यावर्गाहतैः क्रमात् ॥चापं फलानि चाधोऽधो न्यस्योपर्युपरित्यजेत् । जीवापत्यै संग्रहोऽस्यैव विद्वान् इत्यदिना कृतः ॥ Multiply the arc by …
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Fun with Sankalitas – Part 2
Previously, we saw the मूलसङ्कलितम् and also noted that as n becomes large, . We also saw the समघातसङ्कलितानि, sums of higher powers, including the sum of squares – वर्गसङ्कलितम्, and sum of cubes – घनसङ्कलितम्. We noted that in the limit of large n, the kth power sankalita tends to: We also saw सङ्कलितसङ्कलितम्, …
Improving the jyā table
Recap In the previous article in this series, we saw how Āryabhaṭa’s jyā table was calculated. It was a remarkably simple recurrence relation, with accuracy to one minute of arc (using the Indian standard circle of circumference 21600′) at 24 points 225′ apart. प्रथमाच्चापज्यार्धाद्यैरूनं खण्डितं द्वितीयार्धम् ।तत्प्रथमज्यार्धांशैस्तैस्तैरूनानि शेषाणि ।। We set both first jyā B1 …
