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2025-06-10

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Netherlands opt to bowl
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2025-06-10
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2025-06-10
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2025-06-10
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Mumbai South Central Maratha Royals need 123 runs
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2025-06-10

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2025-06-10
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2025-06-10

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2025-06-10

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2025-06-08

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Day 2: Stumps - South Africa A lead by 104 runs
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2025-06-07
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2025-06-06
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2025-06-05
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2025-06-10
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Ratnagiri Jets won by 67 runs
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2025-06-09
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2025-06-09

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2025-06-09

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2025-06-09
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2025-06-09
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2025-06-09

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Norway won by 22 runs
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2025-06-09
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2025-06-08
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2025-06-08

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2025-06-08

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2025-06-08

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2025-06-08

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2025-06-08

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2025-06-08

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2025-06-08

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2025-06-08

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2025-06-08
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2025-06-08

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2025-06-08
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2025-06-08

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Nigeria Women won by 36 runs
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2025-06-08

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Scotland won by 2 runs
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2025-06-08
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2025-06-08
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Salem Spartans won by 6 wkts
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2025-06-08

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2025-06-08

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2025-06-08

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Tanzania Women won by 9 wkts
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2025-06-08

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2025-06-08
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Philippines Women won by 9 wkts
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2025-06-08
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NaMo Bandra Blasters won by 8 wkts
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2025-06-08

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China Women won by 7 wkts
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2025-06-07

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Worcestershire won by 25 runs
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2025-06-07

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Jersey won by 3 runs
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2025-06-07
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2025-06-07
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2025-06-07
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Nellai Royal Kings won by 5 wkts
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2025-06-07
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2025-06-07

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2025-06-07

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2025-06-07
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2025-06-07

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England Women won by 9 wkts (Match reduced to 21 overs per side due to rain, DLS target 106)
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2025-06-07
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2025-06-07

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Jersey won by 7 wkts (DLS Method due to rain)
t20
2025-06-07
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Kolhapur Tuskers won by 7 wkts
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2025-06-07

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Serbia won by 3 runs
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2025-06-07

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Sierra Leone Women won by 4 wkts
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2025-06-07

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Uganda Women won by 7 wkts
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2025-06-07
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Hong Kong Women won by 7 wkts
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2025-06-07
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Eagle Nashik Titans won by 8 wkts - 2nd innings reduced to 5 overs due to rain (Target : 54)
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2025-06-07

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Japan Women won by 59 runs
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2025-06-06

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England won by 21 runs
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2025-06-06

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Northamptonshire won by 31 runs
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2025-06-06

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Somerset won by 7 wkts
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2025-06-06

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Leicestershire won by 6 runs
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2025-06-06

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Surrey won by 42 runs
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2025-06-06

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Hampshire won by 7 wkts
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2025-06-06

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Glamorgan won by 6 wkts
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2025-06-06

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Nottinghamshire won by 7 wkts (DLS method)
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2025-06-06

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Warwickshire won by 6 wkts
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2025-06-06

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Guernsey won by 13 runs (DLS method)
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2025-06-06
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Match tied - Bilaspur Bulls won the Super Over
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2025-06-06

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Chepauk Super Gillies won by 8 wkts
t20
2025-06-06
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Mumbai South Central Maratha Royals won by 6 wkts
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2025-06-06

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Rwanda Women won by 40 runs
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2025-06-06

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Malawi Women won by 6 wkts
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2025-06-06

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Scotland won by 44 runs
test
2025-06-06

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Match drawn
t20
2025-06-06
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Puneri Bappa won by 8 wkts - Match reduced to 8 overs due to rain, DLS target 71
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2025-06-06

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Uganda Women won by 10 wkts
t20
2025-06-06
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Philippines Women won by 118 runs
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2025-06-06

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Japan Women won by 24 runs
t20
2025-06-05

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No Result due to rain
t20
2025-06-05

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Hampshire won by 15 runs (DLS method)
t20
2025-06-05
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Triumphs Knights MNE won by 5 wkts
t20
2025-06-05

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Dindigul Dragons won by 7 wkts
t20
2025-06-05
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SoBo Mumbai Falcons won by 9 wkts
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2025-06-05

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Nigeria Women won by 2 wkts
t20
2025-06-05

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Rwanda Women won by 49 runs
t20
2025-06-05
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Eagle Thane Strikers won by 97 runs
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2025-06-05
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Raigad Royals won by 24 runs
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2025-06-05

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Cameroon Women won by 23 runs
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2025-06-05
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China Women won by 7 wkts
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2025-06-05

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There is no scorecard available for this match.
Widget
Tuesday, August 23, 2011
The Madhava Trignometric Series
The Madhava Trignometric series is one one of a series in a collection of infinite series expressions discovered by Madhava of Sangramagrama ( 1350-1425 ACE ), the founder of the Kerala School of Astronomy and Mathematics. These are the infinite series expansions of the Sine, Cosine and the ArcTangent functions and Pi. The power series expansions of sine and cosine functions are called the Madhava sine series and the Madhava cosine series.
The power series expansion of the arctangent function is called the Madhava- Gregory series.
The power series are collectively called as Madhava Taylor series. The formula for Pi is called the Madhava Newton series.
One of his disciples, Sankara Variar had translated his verse in his Yuktideepika commentary on Tantrasamgraha-vyakhya, in verses 2.440 and 2.441
Multiply the arc by the square of the arc, and take the result of repeating that (any number of times). Divide (each of the above numerators) by the squares of the successive even numbers increased by that number and multiplied by the square of the radius. Place the arc and the successive results so obtained one below the other, and subtract each from the one above. These together give the jiva, as collected together in the verse beginning with "vidvan" etc.
Rendering in modern notations
Let r denote the radius of the circle and s the arc-length.
The following numerators are formed first:
s.s^2,
s.s^2.s^2
s.s^2.s^2.s^2
These are then divided by quantities specified in the verse.
1)s.s^2/(2^2+2)r^2,
2)s. s^2/(2^2+2)r^2. s^2/4^2+4)r^2
3)s.s^2/(2^2+2)r^2.s^2/(4^2+4)r^2. s^2/(6^2+6)r^2
Place the arc and the successive results so obtained one below the other, and subtract each from the one above to get jiva:
Jiva = s-(1-2-3)
When we transform it to the current notation
If x is the angle subtended by the arc s at the center of the Circle, then s = rx and jiva = r sin x.
Sin x = x - x^3/3! + x^5/5! - x^7/7!...., which is the infinite power series of the sine function.
By courtesy www.wikipedia.org and we thank Wikipedia for publishing this on their site.
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