How about explaining math through #cricket? Let’s talk about it in story #29.
Well, apart from Cricketmatics <Check out the link in the comments section>, I came across this:
“In their original paper, G.H. Hardy and J.E. Littlewood explained their maximal inequality in the language of cricket averages.”
Intrigued by this statement, I dug a little deeper and was surprised that the 2 great mathematicians had indeed put forward the Hardy-Littlewood #Maximal #Function in the cricketing parlance.
Their thought experiment involving cricket went like this:
Suppose a batsman scores 20, 100, 30, 40, 70, and 0 in his last six innings (0 being the most recent). Being upset at scoring 0 in his last innings, he might say to himself -- at least I am averaging 35 in my last two innings; or going further, that I'm averaging 36.67 in my last three; or averaging 35 in my last four; or 48 in my last five; or 43.33.
Probably he would most prefer the fifth statement which gives the largest average or the most satisfaction.
Suppose now the batsman does this over an entire season of cricket after each innings computing his satisfaction until then.
Call the total satisfaction the sum of the satisfactions after each innings in the season. Then for a given stock of scores in a season, the Hardy-Littlewood maximal theorem gives that the batsman's total satisfaction is a maximum if his scores are in descending order throughout the series -- or in other words, his satisfaction is a maximum precisely when his batting has been in decline throughout the season!
There is a nice discussion of this in Béla Bollobás’ problem book "The art of mathematics: coffee time in Memphis" -- see problem 85 on Satisfied Cricketers: the Hardy-Littlewood maximal theorem there.
Some more cric-facts to leave you pondering:
1. Looking at every innings by the most prolific batsmen in test history the most common score is zero and by quite a long way too <check out the chart>.
2. What are the odds of a bowler taking all the 10 wickets in an innings and at the same time, the same umpire is officiating at the bowler’s end when those 10 wickets were falling?
Well, on February 7, 1999 - #AnilKumble became the first Indian bowler to bag 10 wickets in an innings. Coincidentally, it was umpire A.V. #Jayaprakash who declared all the 10 Pakistan batsmen out!
Well, cricket does have its romantic relationship with math - doesn’t it?!
Sources:
<1> Cricket and the Hardy-Littlewood maximal function - Mathoverflow.
<2> When cricket meets math by Dilip D’Souza for Livemint.
<3> The art of mathematics: coffee time in Memphis by Béla Bollobás.
<4> The Plus sports page: The curse of the duck - Plus magazine.
#math #mathstories #story29 #cricket #hardy #littlewood #duck #zero
Well, apart from Cricketmatics <Check out the link in the comments section>, I came across this:
“In their original paper, G.H. Hardy and J.E. Littlewood explained their maximal inequality in the language of cricket averages.”
Intrigued by this statement, I dug a little deeper and was surprised that the 2 great mathematicians had indeed put forward the Hardy-Littlewood #Maximal #Function in the cricketing parlance.
Their thought experiment involving cricket went like this:
Suppose a batsman scores 20, 100, 30, 40, 70, and 0 in his last six innings (0 being the most recent). Being upset at scoring 0 in his last innings, he might say to himself -- at least I am averaging 35 in my last two innings; or going further, that I'm averaging 36.67 in my last three; or averaging 35 in my last four; or 48 in my last five; or 43.33.
Probably he would most prefer the fifth statement which gives the largest average or the most satisfaction.
Suppose now the batsman does this over an entire season of cricket after each innings computing his satisfaction until then.
Call the total satisfaction the sum of the satisfactions after each innings in the season. Then for a given stock of scores in a season, the Hardy-Littlewood maximal theorem gives that the batsman's total satisfaction is a maximum if his scores are in descending order throughout the series -- or in other words, his satisfaction is a maximum precisely when his batting has been in decline throughout the season!
There is a nice discussion of this in Béla Bollobás’ problem book "The art of mathematics: coffee time in Memphis" -- see problem 85 on Satisfied Cricketers: the Hardy-Littlewood maximal theorem there.
Some more cric-facts to leave you pondering:
1. Looking at every innings by the most prolific batsmen in test history the most common score is zero and by quite a long way too <check out the chart>.
2. What are the odds of a bowler taking all the 10 wickets in an innings and at the same time, the same umpire is officiating at the bowler’s end when those 10 wickets were falling?
Well, on February 7, 1999 - #AnilKumble became the first Indian bowler to bag 10 wickets in an innings. Coincidentally, it was umpire A.V. #Jayaprakash who declared all the 10 Pakistan batsmen out!
Well, cricket does have its romantic relationship with math - doesn’t it?!
Sources:
<1> Cricket and the Hardy-Littlewood maximal function - Mathoverflow.
<2> When cricket meets math by Dilip D’Souza for Livemint.
<3> The art of mathematics: coffee time in Memphis by Béla Bollobás.
<4> The Plus sports page: The curse of the duck - Plus magazine.
#math #mathstories #story29 #cricket #hardy #littlewood #duck #zero
