An in(cr)edible recipe_Part_002 <3 :)

(This is the 2'nd & final episode of a mysterious piece of pattern....read the first, crucial part here )

Phew...!!!

Finally...! :-)

The time has come...and due to inspirations in various forms...i've finally come "round" to breaking this long suspense over my recip(i)e...fer well...see it below..!

I have talked about a special function f(n) in my previous post 

Now you may be wondering what is so special about it..

Isn't it..??

Have you EVER wondered WHY or HOW the famous mathematical constant, the transcendental number of Pi is usually said to be 22/7 right frem (y)our school days...?

Well, HOLD your breath...& click on the below image I created...(finally, after 4-5 days of being "stuck", "lost", & suddenly getting the solution to generate in one simple line of code..!! :) )...

I shall NOT say ANything ELSE/MORE...!

Just Click, & I'm sure you'll Smile...!! :)

Isn't this one of the MOST surPrising of oLL algorithms/patterns..!??!

The result above is NOT a fluke or co-incidence..

We get even better approximations to Pi at n=5076, etc...& it hovers quite near the value of Pi...as n increases..

I am not aware of ANY Proof as such as to WHY or HOW this ratio seems to approach or approximate Pi the way it does...

[But the max i know is that it could have been discovered by the great genius of Pál Erdős alongwith one of his beloved friends...though I'll surely update this space with more accurate info., as soon as i 'remember' it...!! :) ]

Whatever it is...!!

This is ONE Pi(e) recipe...that is unlike No/few other...!!!

And I'm presently thinking of scribbling a book-let at-least with a cellection of the Greatest such recipes...!!!

WHAT do you say pa..!??! :)

Please say something..!?!?

Come on now...please do respond to me...!! :-(:::

Why, aren't you my sweetie Pi(e)..!?!? ;-) :)...Hmmm...??? 

Take care...& keep smiling..! :)

Lots of LoVE <3 :),

The moron in 'rags'

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"If numbers are not beautiful, 
 I don't know what is."

:-Pál Erdős

I leave you with such a cute, yet beautiful piece frem 'Peanuts' courtesy of Charles Schulz

[click on it...to read it & smile...& please keep smiling..!! ]

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An in(cr)edible recipe_Part_001 <3 :)

Hi pa..!!

Please Listen to Me...at-least one time...!?!

{ Time is running out..!! Hope you ARE listening...!? :-/ Hmmm.. :-( }

I just want you to do something fer me, & I promise YOU to show you something so incredible..!!!! :)

If I give you a +ve integer, 'n' to start with, you should go on giving me the smallest integer that is a multiple of (n-1) such that it is greater than or equal to 'n', STORE the result, & go on till you reach n=2, at which point the result does NOT change...

Okay..? :) 

JUST do that, and I shall show you a MAGICAL new thingy...!! :)
But don't stop...continue with this value 6 & the value 3 as your new 'n'...
i.e.., 6 gives way to 3-1=2*3=6 (n-1 is now 2)
and now, you can verify that considering n=2 , the answer remains the same =  6

Hence, given n=4 the final answer should be 6.
i.e.., 6 gives way to 3-1=2*3=6 (n-1 is now 2)
and now, you can verify that considering n=2 , the answer remains the same =  6
Hence, given n=4 the final answer should be 6.
Hence, given n=4 the final answer should be 6.
Or...to take another example, given n=5, the answer should be 10
{5-->8(by 4)-->9(by 3)-->10(by 2)-->10(by 1)-->STOP}

E.g., fer n=4, u start, & first come up with 6 (temporary result) by considering (n-1)=3

Or....given n=10, the answer should be 34. 

HOW..?

Here's HOW...

{10-->18(by 9)-->24(by 8)-->28(by 7)-->30(by 6)-->30(by 5)-->32(by 4)-->33(by 3)-->34(by 2)-->34(by 1)-->STOP}

So LET us imagine this PROCESS of generating the ANSWER, given a +ve integer 'n' input...as a Black-box...!

In Mathematical terms...let me call it a Function 'f' mapping an input 'n' (+ve integer) to some other +ve integer.

Thus, we have, 

f(1)=1,

f(4)=6,

f(5)=10,

f(10)=34

:

:

and so on...

[Can u write a simple function or manually build a table like this..for different values of +ve integers..?]

AHEM..!!

JUSST keep this function in mind...be READY..!!

For WHAT I shall unveil to YOU...is going to be one amazing surprise...!!!!!

I Promise..!!!!

(To be continued. . .)

[
PS: 

Not that I want to keep you waiting...no way...I myself can't wait...!! 

As I have said, Time is running out...& i have to SHARE soo many beautiful thingies..!!

It's just that I may have to spend some more energy/focus on R&D...! :)

I shall try & come up with a 'black-box' (function) of my own & try to graph some results...which shall be a fitting tribute to this incredible thingy we're going to witness..!

Am sure you shall agree...SOOON....!! ;) :)

Get Ready...to be SURPRISED...!!!

]