THE SCIENCE OF CRICKET

They are not just cricketers but intellectuals...

The Gul effect:

In 1852 Heinrich Magnus formulated the Magnus effect which explains the motion of a projectile when experiencing different pressures, hence effectively explaining reverse swing. Umar Gul went a step further, investigating the effect of pace on such a projectile. He found a deadly positive correlation between the two and also discovered that overcast conditions would assist as well. He conducted his initial experiments in England at the Brit oval to devastating effect. Many of his test subjects had crushed toes.

Shehzad’s theory of small quanta:

The rare big quantum.

The quantum theory predicted that energy traveled more like packets than as a continuous wave. Ahmed Shehzad suggested that performances also followed the same pattern. He also formulated that most of these quanta were small with an occasional big quantum. When asked about the probability of these big quanta occurring, he said after much deliberation, ''when He wills’’. When also questioned about people like Hashim Amla and Tendulkar, he disdainfully quipped, ‘’abnormalities’’.  

Khan's charge discharge theory:

He's just discharging...energy.

Shahid Afridi suggested that the most efficient way to discharge pent up energy is to stand like a lightning rod with the index fingers pointing up. The charge discharged in such a posture, in one second, with the feet a metre apart, is known as a khan. SI unit Kh. 

Khan's theory of drift:


This is the counterpart of the Gul effect with a spinning ball bowled at considerable pace.Despite having few adherents, the devastating capability of this theory is not doubted. The pioneer again is the hugely talented Shahid Afridi. Rumor has it that Abdul Razzaq is considering the option of become a spinner to get that much-wanted movement. 




Akmal's hypothesis of error: 

One of those days.

On some days, the probability of error is 1.

MATHS: THE LANGUAGE

Finally a blog where I can easily find a niche. I usually write on dull, sordid affairs on how humanity has to improve; today its something entirely different . I am in love ( did I break some hearts?). In love with a language so beautiful that words could only undermine its lineaments( aah you're breathing again. just a language). Flirting with it has been my passion of late. A recent flirtation proved immensely satisfying, the results of which I will share today and hopefully future flirtations will also come up on this blog. 


THE ROOT OF IT...


Now to business. Some days ago I was idly wondering if a square root of some number could be found without the use of a calculator. I scribbled a lot and did end with something material. Suppose a number say, 131. The average mathematician could (and should) limit the root of this number to be somewhere between 11 and 12, since 11^2 is 121 while 12^2 is 144. Using a crude number line, the result can be presented as:




(11)^2.....................131.........................................(12)^2




The 'distance' from 131 to 11^2 is 10. And the 'distance' from (12)^2 to (11)^2  is 23. Working on the fractional theory the root will approximately be 11+ (10/23), which works out to 11.438. The actual answer is 11.445. Pretty close. But creating such a number line is tedious. What we need is a more compact and general formula.




Let us then say that the lower limit we use be 'a'( 11 in the above example) and the upper limit be 'b' (12 in the above example). Let the number for which the root is being calculated, be 'n'. The general form we thus derive is:




                             a +  {[n-(a)^2] / [ (b)^2 - (a)^2 ]}






But we know that (b)^2 - (a)^2 = [b-a] [b+a]. AND we also know that 'b' and 'a' are consecutive, thus [b-a] = 1. Thus, simplified:


                        
                               a +  {[n-(a)^2] / [ b + a ]}




(NOTE: This result is the most useful one as far as time is concerned.)




A mathematician is a perfectionist. And he does not like two functions if one could be made. Take the LCM of this function and get: 




                                  [ab + n]/ [a+b]


An example: *313* ( under root 313)


a = 17 , b = 18 , n = 313


                            [(17) (18)+ 313] / [17+ 18 ] = 17.685~ 17.69




actual calculated answer = 17.691


              






This a hot looking formula isn't it? It will give you answers to usually  1 dp (sometimes 2). However, there are limitations. This requires some pre-knowledge of perfect squares. The extent of that knowledge would define the use. I know squares of numbers upto 20 comfortably and thus I am limited to using this formula for n < or = 400. If you are to know squares upto 30, you can go all the way up to 900. Also, this theory does not work well with small numbers like n= 3. Its accuracy will go up as the value of n goes up. To somehow cover up that limitation I introduced a 'fixer'.






I found that all my answers from this theory were LESSER than the actuals. So I had to add something to increase accuracy. the fixer I settled upon was [0.1 (a) / n]. So if you are an accuracy freak the formula would then be:




                              [ab + n]/ [a+b] +  [0.1 (a) / n]






So there it is. A special thanks to some people. Wajahat Hasan for lending his ear ( despite his constant skepticism that I had plagiarized this:P), Saad Salim for his 'bht tyt' , Hasan Nagaria for influencing the initial para and Tanzeel Huda for awaiting this ( I hope you like this). Next time: something about the most beautiful number in the world. 




Trivia:(Here I'm missing another form of equation that could be made. Can you come up with it??:P)




NO PART OF THIS THEORY IS PLAGIARISED. IF SOMEONE DOES FIND IT OFF THE NET, DO INFORM.