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Wednesday, February 29, 2012

Aryabhatta and origin of zero


Aryabhatta (476-550 A.D.), one of the world’s greatest mathematician-astronomer, was born in Patliputra in Magadha, modern Patna in Bihar. Many are of the view that he was born in the south of India especially Kerala and lived in Magadha at the time of the Gupta rulers. However, there exists no documentation to ascertain his exact birthplace. Whatever this origin, it cannot be argued that he lived in Patliputra where he wrote his famous treatise the "Aryabhatta-siddhanta" but more famously the "Aryabhatiya", the only work to have survived.

The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry and spherical trigonometry. It also contains continued fractions, quadratic equations, sums of power series and a table of sines. This work is the first we are aware of which examines integer solutions to equations of the form by = ax + c and by = ax - c, where a, b, c are integers. Aryabhatta was an author of at least three astronomical texts and wrote some free stanzas as well.

He wrote that if 4 is added to 100 and then multiplied by 8 then added to 62,000 then divided by 20,000 the answer will be equal to the circumference of a circle of diameter twenty thousand. This calculates to 3.1416 close to the actual value Pi (3.14159).

But his greatest contribution has to be ZERO, for which he became immortal. He certainly did not use the symbol, but the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients. The supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.

He already knew that the earth spins on its axis, the earth moves round the sun and the moon rotates round the earth. He talks about the position of the planets in relation to its movement around the sun. He refers to the light of the planets and the moon as reflection from the sun. Aryabhatta gives the radius of the planetary orbits in terms of the radius of the Earth/Sun orbit as essentially their periods of rotation around the Sun. He believes that the Moon and planets shine by reflected sunlight, incredibly he believes that the orbits of the planets are ellipses. He correctly explains the causes of eclipses of the Sun and the Moon.

This remarkable man was a genius and continues to baffle many mathematicians of today. His works was then later adopted by the Greeks and then the Arabs.

Bhaskara I who wrote a commentary on the Aryabhatiya about 100 years later wrote of Aryabhatta:-
"Aryabhatta is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world."

Who is the inventor of television?

Who is the inventor of television? You have really opened up a can of worms with that question! Probably no other invention in history has been so hotly disputed as the prestigious claim to the invention of 'Tele-vision or 'long-distance sight' by wireless.”

Since Marconi’s invention of wireless telegraphy in 1897, the imagination of many inventors have been sparked with the notion of sending images as well as sound, wirelessly. The first documented notion of sending components of pictures over a series of multiple circuits is credited to George Carey. Another inventor, W. E. Sawyer, suggested the possibility of sending an image over a single wire by rapidly scanning parts of the picture in succession.

On December 2, 1922, in Sorbonne, France, Edwin Belin, an Englishman, who held the patent for the transmission of photographs by wire as well as fiber optics and radar, demonstrated a mechanical scanning device that was an early precursor to modern television. Belin’s machine took flashes of light and directed them at a selenium element connected to an electronic device that produced sound waves. These sound waves could be received in another location and remodulated into flashes of light on a mirror.

Up until this point, the concept behind television was established, but it wasn’t until electronic scanning of imagery (the breaking up of images into tiny points of light for transmission over radio waves), was invented, that modern television received its start. But here is where the controversy really heats up.

The credit as to who was the inventor of modern television really comes down to two different people in two different places both working on the same problem at about the same time: Vladimir Kosma Zworykin, a Russian-born American inventor working for Westinghouse, and Philo Taylor Farnsworth, a privately backed farm boy from the state of Utah.

“Zworykin had a patent, but Farnsworth had a picture…”

Zworykin and his televisionZworykin is usually credited as being the father of modern television. This was because the patent for the heart of the TV, the electron scanning tube, was first applied for by Zworykin in 1923, under the name of an iconoscope. The iconoscope was an electronic image scanner - essentially a primitive television camera. Farnsworth was the first of the two inventors to successfully demonstrate the transmission of television signals, which he did on September 7, 1927, using a scanning tube of his own design. Farnsworth received a patent for his electron scanning tube in 1930. Zworykin was not able to duplicate Farnsworth’s achievements until 1934 and his patent for a scanning tube was not issued until 1938. The truth of the matter is this, that while Zworykin applied for the patent for his iconoscope in 1923, the invention was not functional until some years later and all earlier efforts were of such poor quality that Westinghouse officials ordered him to work on something “more useful.”

Baird and his mechanical televisionAnother player of the times was John Logie Baird, a Scottish engineer and entrepreneur who 'achieved his first transmissions of simple face shapes in 1924 using mechanical television. On March 25, 1925, Baird held his first public demonstration of 'television' at the London department store Selfridges on Oxford Street in London. In this demonstration, he had not yet obtained adequate half-tones in the moving pictures, and only silhouettes were visible.' - MZTV

In the late thirties, when RCA and Zworykin, who was now working for RCA, tried to claim rights to the essence of television, it became evident that Farnsworth held the priority patent in the technology. The president of RCA sought to control television the same way that they controlled radio and vowed that, “RCA earns royalties, it does not pay them,” and a 50 million dollar legal battle subsequently ensued.

Farnsworth with his televisionIn the height of the legal battle for patent priority, Farnsworth’s high school science teacher was subpoenaed and traveled to Washington to testify that as a 14 year old, Farnsworth had shared his ideas of his television scanning tube with his teacher.

With patent priority status ruled in favor of Farnsworth, RCA for the first time in its history, began paying royalties for television in 1939.

Philo Farnsworth was recently named one of TIME Magazine's 100 Greatest Scientists and Thinkers of the 20th Century.

Brian Lara


Picture of Brian Lara

Brian Lara

Batting style:
Left Handed bat
Bowling style:
Leg break
Played for:
West Indies Under-19, West Indies, ICC World XI, Mumbai Champs
Skipper-Test,ODI | Batsman

Profile

One look at Brian Charles Lara's Test scores, and there is no doubt in one's mind that here is a batsman with a vociferous appetite for runs. In the year 1994, he broke his countryman Gary Sobers' long standing record for many decades by scoring a brilliant 375. As if to prove that this was not a fluke, he followed it up with an unbeaten 501 in a first class match for Warwickshire the following season. In 2004, Lara became the first batsman to reclaim the highest individual Test score record by scoring a 400 against England, in the process breaking Hayden's 380.

Lara's attitude towards cricket can be best described as moody brilliance. To go with the above records, he is probably the only batsman to have tackled Murali the way he did, scoring 600-odd runs in a three match series in Sri Lanka, his innings epitomized by quicksilver feet movement. And then there were times, when he looked good to be anywhere but the batting crease, almost as if his mind's not on the job. As if to drive home a point, Lara's overall Test average of almost 53 is not too dissimilar from his 51 against the Aussies, and it was only 41 against NZ.

Brian Lara's ODI record of more than 10,000 runs at an average of almost 41 was equally great, but somehow, his amazing Test innings overshadowed the same. Incidentally, Lara became the second batsman, after Sachin Tendulkar to score more than 10,000 runs in both forms of the game

On retirement, Lara is one of the few cricketers, whose Test average was more than his First Class one!

Statistics

Show:
  Matches Innings Runs NO Avg. SR 100's 50's HS
Test 131 232 11953 6 52.88 60.50 34 48 400*
ODI 299 289 10405 32 40.48 79.51 19 63 169

Career

Span:
Test:
1990-2006
 
ODI:
1990-2007
Test
Debut:
West Indies Vs Pakistan at Gaddafi Stadium (Lahore Stadium), Lahore - Dec 06, 1990
Last played:
West Indies Vs Pakistan at National Stadium, Karachi - Nov 27, 2006
ODI
Debut:
West Indies Vs Pakistan at National Stadium, Karachi - Nov 09, 1990
Last played:
West Indies Vs England at Kensington Oval, Bridgetown - Barbados - Apr 21, 2007
 

ODI Batting and Bowling

ODI Batting
             
 Matches  Innings  Runs  Average  HS  100  50
 453 442 18111 45.16 200* (SA) 48 95
             
 
ODI Bowling






 Overs  Runs  Wicket  Average  Best  5w
 1340.4 6838  154 44.40  5-32  2

ODI Centuries

 
S No Runs Against Venue Year
01 110 Australia Colombo 1994 
02 115 New Zealand Baroda 1994 
03 105 West Indies Jaipur 1994
04 112* Sri Lanka Sharjah 1995 
05 127* Kenya Cuttack 1996
06 137 Sri Lanka Delhi 1996
07 100 Pakistan Singapore 1996 
08 118 Pakistan Sharjah 1995 
09 110 Sri Lanka Colombo 1996
10 114 South Africa Mumbai 1996
11 104 Zimbabwe Benoni 1997 
12 117 New Zealand Bangalore 1997 
13 100 Australia Baroda 1998 
14 142 Australia Sharjah 1998 
15 132 Australia Sharjah 1998 
16 100* Kenya Calcutta 1998 
17 128 Sri Lanka Colombo 1998 
18 127* Zimbabwe Bulawayo 1998 
19 141 Australia Dhaka 1998 
20 118* Zimbabwe Sharjah 1998 
21 124* Zimbabwe Sharjah 1998 
22 140* Kenya Bristol 1999 
23 120* Sri Lanka Colombo 1999 
24 186* New Zealand Hyderabad 1999 
25 122 South Africa Baroda 2000 
26 101 Sri Lanka Sharjah 2000 
27 146 Zimbabwe Jodhpur 2000 
28 139 Australia Indore 2001 
29 122* West Indies Harare 2001 
30 101 South Africa Johannesburg 2001 
31 146 Kenya Paarl 2001 
32 105* England Chester-le-Street 2002
33 113 Sri Lanka Bristol 2002
34 152 Nambab Pietermaritzburg 2003
35 100 Australia Gwalior 2003
36 102 New Zealand Hyderabad 2003
37 141 Pakistan Rawalpindi (d/n) 2004
38 123 Pakistan Ahmedabad 2005
39 100 Pakistan Peshawar 2006
40 142* West Indies Kuala Lumpur 2006
41 100* West Indies Vadodara 2007
42 117* Australia Sydney 2008
43 163* New Zealand Christchurch 2009
44 138 Sri Lanka Colombo (RPS) 2009
45 175 Australia Hyderabad (Ind) 2009
46 200* South Africa Gwalior 2010
47 120 England Bangalore 2011
48 111 South Africa Gwalior 2011

ODI Milestones

Mts Runs Age Opponents Venue Season
36 1000 18 yrs & 318 days Zimbabwe Hamilton 1991-92
73 2000 20 yrs & 354 days UAE Sharjah 1993-94
96 3000 21 yrs & 350 days Sri Lanka Sharjah 1994-95
115 4000 22 yrs & 359 days South Africa Sharjah 1995-96
141 5000 23 yrs & 294 days South Africa Durban 1996-97
176 6000 24 yrs & 265 days Pakistan Dhaka 1997-98
196 7000 25 yrs & 74 days Sri Lanka Colombo 1998-99
217 8000 26 yrs & 45 days Pakistan Manchester 1999
242 9000 26 yrs & 330 days South Africa Nagpur 1999-00
266 10000 27 yrs & 341 days Australia Indore 2000-01
284 11000 28 yrs & 279 days England Kanpur 2001-02
309 12000 29 yrs & 311 days Pakistan Centurion 2002-03
330 13000 30 yrs & 327 days Pakistan Rawalpindi 2003-04
359 14000 32 yrs & 288 days Pakistan Peshawar 2005-06
387 15000 34 yrs & 66 days South Africa Belfast 2007
409 16000 34 yrs & 287 days Sri Lanka Brisbane 2008
435 17000 36 yrs & 195 days Australia Hyderabad 2009
451 18000 37 yrs & 334 days Australia Ahmedabad 2011
453 18111 37 yrs & 343 days Sri Lanka Mumbai 2011
<< Go Back
Last Updated 03 April 2011

ODI Venue

ODI Venue-Based









 S No
Mat I No Runs HS Ave 100s 50s
 1 Home 164 160 15 6976 200* 48.11 20 38
 2 Away 143 143 10 4932 163* 37.06 11 24
 3 Neutral 146 140 16 6203 152 50.02 17 33
  Overall 453 442 41 18111 200* 45.16 48 95

ODI Venue-Based









 S No
Mat I No Runs HS Ave 100s 50s
 1 As captain 73 70 5 2424 186* 37.75 6 12
 2 Not as Captain 380 372 36 15657 200* 46.59 42 83
 3 Matches Won 230 227 34 11012 200* 57.05 33 58
 4 Matches Lost 195 195 2 6430 175 33.31 12 35
 5 Matches W/No Results 24 16 5 518 105* 47.09 1 1
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Last Updated 03 April 2011

Sachin's ODI Stats

 S No  Opponents Mat I No Runs HS Ave 100 50
 1  Australia 68 67 1 3058 175 46.33 9 15
 2  Bangladesh 11 10 1 382 82* 42.44 0 2
 3  Bermuda 1 1 1 57* 57* - 0 1
 4  England 37 37 4 1455 105* 41.71 2 10
 5  Ireland 2 2 0 42 38 21.00 0 0
 6  Kenya 10 9 3 647 146 107.83 4 1
 7  Namibia 1 1 0 152 152 152.00 1 0
 8  Netherlands 2 2 0 79 52 39.50 0 1
 9  New Zealand 42 41 3 1750 186* 46.05 5 8
 10  Pakistan 68 66 4 2474 141 39.16 5 15
 11  South Africa 57 57 1 2001 200* 35.75 5 8
 12  Sri Lanka 79 75 9 2983 138 45.19 8 17
 13  U.A.E 2 2 0 81 63 40.50 0 2
 14  West Indies 39 39 9 1573 141* 52.43 4 11
 15  Zimbabwe 34 33 5 1377 146 49.17 5 5

 Overall 453 442 41 18111 200* 45.16 48 95
<< Go Back
Last Updated 03 April 2011

Sachin Tendulkar pictures 5

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Film City, Mumbai  Located in a secluded area in the vicinity of Aarey Colony,  Mumbai , Film City is often regarded as a home ...