 |
|
| |
|
|
|
at Global Oneness Community.
Share your dreams and let others help you with the interpretation!
Dream Sharing Forum
|
|
Madhava of Sangamagrama - Contributions | | Madhava of Sangamagrama - Contributions: Encyclopedia II - Madhava of Sangamagrama - Contributions | | He discovered the infinite series for arctan and sin and many methods for calculating the circumference of the circle.
One of Madhava's series is known from the text Yuktibhasa which describes -
The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc. The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. All the terms are then divided by the odd num ...
See also:Madhava of Sangamagrama, Madhava of Sangamagrama - Contributions, Madhava of Sangamagrama - Kerala School of Astronomy and Mathematics | | | Madhava of Sangamagrama, Madhava of Sangamagrama - Contributions, Madhava of Sangamagrama - Kerala School of Astronomy and Mathematics, Indian mathematicians, Mathematical analysis, Calculus, History of Calculus, Parameswara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri, Achyuta Panikkar. | | |
| | | Madhava of Sangamagrama: Encyclopedia II - Madhava of Sangamagrama - Contributions
Madhava of Sangamagrama - Contributions
He discovered the infinite series for arctan and sin and many methods for calculating the circumference of the circle.
One of Madhava's series is known from the text Yuktibhasa which describes -
The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc. The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. All the terms are then divided by the odd numbers 1, 3, 5, .... The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank. It is laid down that the sine of the arc or that of its complement whichever is the smaller should be taken here as the given sine. Otherwise the terms obtained by this above iteration will not tend to the vanishing magnitude.
This yields
which further yields the theorem
,
popularly attributed to James Gregory, three centuries before Gregory. Using this series he gave a value of the number pi:3.14159265359 - correct to 11 decimals.
Other related archives1350, 1425, Achyuta Pisharati, Aryabhatta, Calculus, Cauchy, Indian mathematicians, James Gregory, Jyeshtadeva, Kerala, Kerala school, Mathematical analysis, Melpathur Narayana Bhattathiri, Neelakanta Somayaji, Parameswara, South India, infinity, limit, mathematical analysis, pi
 Adapted from the Wikipedia article "Contributions", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
|
|
|
More material related to Madhava Of Sangamagrama can be found here:
|
|
|
« Back
|
Search the Global Oneness web site |
|
|
|
|
|
Sneak-Peek of Global Oneness Community
Hi friend! The Global Oneness Community, the place for information and sharing about Oneness is not really launched yet (you will see there is still some clean up to do) ...but it is now open for a sneak-peek! And if you wish - please register and become one of the very first members to do so! Jonas
Forum Home,
Articles,
Photo Gallery,
Videos,
News,
Sitemap
...and much more!
|
