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Clarify Virasena's approximation to pi
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(Clarify Virasena's approximation to pi)
Virasena was a noted mathematician. He gave the derivation of the [[volume]] of a [[frustum]] by a sort of infinite procedure. He worked with the concept of ''ardhaccheda'': the number of times a number could be divided by 2; effectively logarithms to base 2. He also worked with logarithms in base 3 (trakacheda) and base 4 (caturthacheda).<ref>{{citation| contribution=History of Mathematics in India|title=Students' Britannica India: Select essays|editor-first1=Dale|editor-last1=Hoiberg|editor-first2=Indu|editor-last2=Ramchandani|first=R. C.|last=Gupta|page=329|publisher=Popular Prakashan|year=2000| contribution-url=http://books.google.co.uk/books?id=-xzljvnQ1vAC&pg=PA329&lpg=PA329&dq=Virasena+logarithm&source=bl&ots=BeVpLXxdRS&sig=_h6VUF3QzNxCocVgpilvefyvxlo&hl=en&ei=W0xUTLyPD4n-4AatvaGnBQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBgQ6AEwATgK#v=onepage&q=Virasena%20logarithm&f=false}}</ref>
 
Virasena gave the approximate formula ''C''&nbsp;=&nbsp;3''d''&nbsp;+&nbsp;(16''d''+16)/113 to relate the circumference of a circle, ''C'', to its diameter, ''d''. For large values of ''d'', this gives the approximation &pi;&nbsp;≈&nbsp;355/113&nbsp;=&nbsp;3.14159292..., which is more accurate than the approximation &pi;&nbsp;≈&nbsp;3.1416 given by [[Aryabhata]] in the ''[[Aryabhatiya]]''.<ref>{{Citation
He was also the first person to give a value of [[pi]] more accurate than provided by any of his predecessors by means of constructing a [[monotonic function|monotonically decreasing]] sequence approaching pi as a [[limit (mathematics)|limit]].<ref>{{Citation
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