I am enumerating the title as I intend to followit up later....for now you might wanna watch the following video from 2.58 to 4.55.
and we wondered how come astrology became a honors course during his tenure as MHRD. Oops i missed the 'Hon'ble' outfront.
Tuesday, April 20, 2010
Saturday, April 10, 2010
Kaprekar's Pattern
Just a little Saturday Afternoon fun.
Take a three digit number and arrange it's digits in ascending number. Call the three digit number that you get N1.Arrange the numbers in descending order and call the three digit number you now get N2.Now subtract N1 from N2. Call this whole procedure iteration one.The resulting three digit number will be 495 (Kaprekar's Constant) after a certain number of iterations.It is 495 since applying the process to that number brings it back to itself.So 495 is the Kaprekar fixed point.(for three digit numbers)
One can start with single and double digit numbers by appending zeros to the front.Infact during the iterations if the result of subtraction comes to be a two digit number then zeros have to be appended outfront to keep the number of digits 3.Not doing that can lead to zero and not the constant (consider the result 99).The process obviously fails for multiples of Nelson.
One can ask if the number of iterations required would be periodic(or have some pattern) in the natural number argument to start the iterations.Rather than work out the algebra (which to me seemed to involve a lot of conditional routes if analytics of the process is possible) I wrote a matlab program (but blogspot does not let me upload it here!) to plot number of iterations required against a user fed limit,N.The maximum number of iterations required for any number is 6 and the least is 1(By definition). (Kaprekar's constant itself needs to be processed once to get back to itself.)
Here's the Graph:
May be connecting the dots would be more appealing (though mathematically absurd since the process requires natural number input and cannot be interpolated).But here it goes:
Is this periodic? Is there any symmetry?what is the period if there is one?
Do four digit numbers settle to such a value ?Yes they do!!! The K constant in this case happens to be 6174.which I discovered reading here. More on this later.
P.S: Just discovered that people at mathematica beat me blue long long back...they have something called the Generalized Kaprekar Routine .(Aagh!!!)
Take a three digit number and arrange it's digits in ascending number. Call the three digit number that you get N1.Arrange the numbers in descending order and call the three digit number you now get N2.Now subtract N1 from N2. Call this whole procedure iteration one.The resulting three digit number will be 495 (Kaprekar's Constant) after a certain number of iterations.It is 495 since applying the process to that number brings it back to itself.So 495 is the Kaprekar fixed point.(for three digit numbers)
One can start with single and double digit numbers by appending zeros to the front.Infact during the iterations if the result of subtraction comes to be a two digit number then zeros have to be appended outfront to keep the number of digits 3.Not doing that can lead to zero and not the constant (consider the result 99).The process obviously fails for multiples of Nelson.
One can ask if the number of iterations required would be periodic(or have some pattern) in the natural number argument to start the iterations.Rather than work out the algebra (which to me seemed to involve a lot of conditional routes if analytics of the process is possible) I wrote a matlab program (but blogspot does not let me upload it here!) to plot number of iterations required against a user fed limit,N.The maximum number of iterations required for any number is 6 and the least is 1(By definition). (Kaprekar's constant itself needs to be processed once to get back to itself.)
Here's the Graph:
May be connecting the dots would be more appealing (though mathematically absurd since the process requires natural number input and cannot be interpolated).But here it goes:
Is this periodic? Is there any symmetry?what is the period if there is one?
Do four digit numbers settle to such a value ?Yes they do!!! The K constant in this case happens to be 6174.which I discovered reading here. More on this later.
P.S: Just discovered that people at mathematica beat me blue long long back...they have something called the Generalized Kaprekar Routine .(Aagh!!!)
Friday, April 9, 2010
Ads/CRT (Not to be confused with Ads/CFT)
Ads on TV can range from irritating to the ridiculous. A case in point being the Snuggly ad:
Do I need say how many Spoofs of this ad you can get among the related videos on youtube?!!!
But sometimes I find them useful in a way the sponsors hardly intend them to be.
They have over the years often introduced me to some of the bands I hear most!!!
This blog is prompted by a very recent discovery of a band called "The Heavy" through the Kia Motors Ad for Sorento.
The catchy background score got me searching for it as it must have many others who had searched for it before me on youtube:
Check out Set me Free and Colleen from the same guys.
Sometime ago through a Lincoln Car Ad I came to know about the "Under the Milky Way Tonight" by Church.
It's a pretty good track except it gets me queasy when she says exactly what the title says "under the milky way".....makes me feel the earth dropped out of it's place in the saucer's plane!!!
Lest you think I run off in search of western tracks only, here's a piece that adult swim plays in the background of it's program schedule.It's a groovy mystic Asian(Indian Sounding) piece:
Another piece that plays against the ad for Sony Bravia is a soothing acoustic piece by Jose Gonzalez:
Once it so happened that I already knew the track that was playing in the background!!!(Of the very few things I know before I am supposed to know.)It was a HTC phone ad.The track being Sinnerman by Nina Simone that I had researched for after watching The Thomas Crown Affair.I find the piece unbelievably exhilarating.
For an interesting discussion of the piece read here.
Finally,to come back to car ads there is this Audi Separation Offical Extended Version, that the creator of the piece says he had to create just cause there was so much enthusiasm for the part that played with the actual commercial.Here's the whole thing:
Having read this far I hope one is able to figure out what the Notation "Ads/CRT" stands for then!Go Figure:)
Do I need say how many Spoofs of this ad you can get among the related videos on youtube?!!!
But sometimes I find them useful in a way the sponsors hardly intend them to be.
They have over the years often introduced me to some of the bands I hear most!!!
This blog is prompted by a very recent discovery of a band called "The Heavy" through the Kia Motors Ad for Sorento.
The catchy background score got me searching for it as it must have many others who had searched for it before me on youtube:
Check out Set me Free and Colleen from the same guys.
Sometime ago through a Lincoln Car Ad I came to know about the "Under the Milky Way Tonight" by Church.
It's a pretty good track except it gets me queasy when she says exactly what the title says "under the milky way".....makes me feel the earth dropped out of it's place in the saucer's plane!!!
Lest you think I run off in search of western tracks only, here's a piece that adult swim plays in the background of it's program schedule.It's a groovy mystic Asian(Indian Sounding) piece:
Another piece that plays against the ad for Sony Bravia is a soothing acoustic piece by Jose Gonzalez:
Once it so happened that I already knew the track that was playing in the background!!!(Of the very few things I know before I am supposed to know.)It was a HTC phone ad.The track being Sinnerman by Nina Simone that I had researched for after watching The Thomas Crown Affair.I find the piece unbelievably exhilarating.
For an interesting discussion of the piece read here.
Finally,to come back to car ads there is this Audi Separation Offical Extended Version, that the creator of the piece says he had to create just cause there was so much enthusiasm for the part that played with the actual commercial.Here's the whole thing:
Having read this far I hope one is able to figure out what the Notation "Ads/CRT" stands for then!Go Figure:)
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