@Preben Alsholm The notice says to contact the author if to use as a for-profit use.  We are not using it for profit.  All we are trying to do is allow the use of it (in it's slightly altered original form) with another package of the same name by renaming it and allowing it to be used under the newer archives at the same time.  I suppose the alternative would be to leave the file alone and change all other FourierSeries package names not copyrighted to something else.  But then that legal notice of being copyrighted screws the rest of us from using packages called FourierSeries at the same time.  In which case the only thing to do is add the path to libname so it can be loaded whenever and then unload it and remove the path from libname when we want to load a different FourierSeries package.

I don't know if there's a problem if we rename the file but still have the author credited.

@NorwegianStudent There's only 3 commands in that package which you can uncover using showstat to show the inner workings.  I don't think there's an easy way to just rename a module, I think one would have to rebuild the module, then save it.  It would be just one file and have the newer extension .mla

@NorwegianStudent you would have to rename one of the packages.  As long as the commands inside the package are different there wouldn't be any clashes. 

Outside of renaming you would have to load and unload each package seperately using shorthand notation as well as changing libname so that Maple wouldn't look in the other library and load the wrong one and vice versa.  Renaming would be the better option.

Renaming the Khanshan FourierSeries to FourierSeriesK for example and the Wilhelm Werner FourierSeries to FourierSeriesW.  Ending with the last initial of the author to reflect whose package you're using.

@NorwegianStudent .. You defnined Coeficients from 0..2Pi and a[n] from -Pi..Pi

Using the package from Mr. Khanshan and your example similar results are obtained

I don't have a problem loading into Maple 2017.  You probably used the wrong slashes (backslash instead of forward slash) in libname

Create a folder under c: drive labelled fs and copy the .ind and .lib into the folder.

Then initiate libname:=libname,"c:\\fs"  Note the forward slashes.

It would be better if Maple could make a better guess with the initial data without having to supply initialvalues.

In this case Maple comes up with the fit if we supply it only with the initial value of A.  We can guess from the plot it's about 45 or so.  

It's probably not that surprising that Maple doesn't come up with a proper fit right away.  But why wasn't Geogebra fooled?  Maybe it's perhaps the algorithm being used in Maple that's too simplified or is it the other way around and actually too complex?

@NorwegianStudent .. using older packages on new software can cause unpredictable results.  I'll have a look shortly, try Preben Alsholm's solution above, perhaps that will work for you instead.

@Christopher2222 someone deleted the zip file I uploaded.  Why?

I'll try again, it belongs with the application in the application center.  Here it is again.

FourierSeriesAndExamples.zip

The package must have been lost during some of the upgrades.

The worksheet does open with Maple 10, however the library package FourierSeries that should have been with the application in the application center is missing.

You could upload your worksheets here and someone might be able to repair it enough to be able to open (I recall a repair on someone's file a while ago).

It's possible you have startup code that points to a database that has moved.

@AmusingYeti  The development of probability theory resulted from the earnest contemplation of problems faced by gamblers. In the 20th century, much progress in computer science resulted from trying to program a machine to play chess.

Recreational math may seem like an oxymoron to some.  The term broadly includes puzzles such as Sudoku where no advanced knowledge of mathematics is required yet still involves the same logic and deductive skills used in mathematics. 

Martin Gardner's Mathematical games in the back of Scientific American I think would be a great example of recreational math.

Majorie rice in 1975, with no math beyond high school discovered four new tessellations, as a result of in my opinion "recreational math".

So by no means should we not consider recreation and math in the same sentence.  Math and Recreational math are both serious business.

The issue is fixed.  Thanks to mapleprimes for addressing the issue.

When I first read the title, I wondered what it meant.  Then I looked into the post and I thought "That's really neat!"

I enjoy the creative side people use to come up with ideas using mathematics/maple.  It's quite an art!

@Markiyan Hirnyk for research?  Cryptographers?  or just plain fun :)

@Kitonum thanks, I didn't know tubeplot would trick the axes.  I did indeed try white earlier, it is invisible unless the modelled shape is behind the axes.