@Carl Love 

thanks a lot Dear Carl Devore for the release of most complete Maple worksheet at this topic !

for help to people Please register and contribute your work in The On-Line Encyclopedia of Integer Sequences

and share the link too ?

I found a similar application in poetry but few details "Sestina"

Indeed there must be a relation between this kind of permutation and Melody or musical features ...

amazin spiral !

@Rouben Rostamian  

thanks a lot for contribution !

but this time wondered that the steps of cycles are so smaller than the number of letters ! (995 and 180)

If we attention to antique and history of cipher ! it is a handy method and don't need machin or computer for calculation ?

@vv 

... discovering great relation !

:(

@vv 

and thanks a lot for your analyze !

and i surprised on the sequence too !!!

I expected that the number of cycle and letter are so close but you showed ( 42 and131072) !!!

i will think about it more and deeper ...

although i had a lot of obsession on various ways and commands that may used by maple to run the algorithm but finally i satisfied with the function as described ...

yet curious to receive more intelligent offers from othere members ?

@Les  I learned a lot from you

please , can you demonstrate how the Nile river flows on curvature of earth ?

thanks a lot

@Kitonum 

you have Treasure ?

@Alsu
I like all of your graphics

BUT ! DO YOU HAVE A MAPLE worksheet for sharing ?

GREAT WORK

@Daniel Skoog 
I Am So Proud Of  Receiving the first announcement , from one of the great professionals of MapleSoft , Daniel Skoog !

I bet many Acclamation by Maple enthusiastic delivered here .

added to my favorits

thanks

https://www.maplesoft.com/products/roadmap.aspx
After MAPLE 18 , every new release stand in more narrow platform ! until this 2019 version that is available only for 64 bit os !
and I personally yet use maple 18 even today on xp and works so great for me , I don't know whether Maplesoft gathered a comprehensive votes of useres on the most popular platforms selected by users ?
I wish MAPLESOFT don't stop making updates for older versions ...

@vv
your sincerely Fereydoon Shekofte
appreciate for spending of your valuable time on students !
Is it right that every kind and form of curves may be demonstrated by Fourier transform or in other words every curve is just some of SINs and COSs ?
If yes, why for approximating the mentioned curve , the Fourier transform did'nt discuss in this case ?

or except polynomial fit and splin interpolation other approaches are available in Maple ?

@vv 

thanks a lot for definition , so far i did'nt see any document that historicaly recorded this link between parabola and dissecting area ...

so this can be a new thesis ?

indeed you are Genius !

your maths are so advanced and i need to think about them some hours ...

i hope by incresing my knowledge i can contribute in your work