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MaplePrimes Activity

These are replies submitted by Earl

@Rouben Rostamian  Thank you for your wonderful analysis and solution to my question. I will take lots of time to analyze it, including substituting my worksheet's river velocity function for yours.

@Carl Love Please see my latest reply to Rouben Rostamian. I hope you too can now access Rivercrossing.mw

@Rouben Rostamian  Following Carl Love's advice I renamed my worksheet as one word and it appears to have uploaded successfully. Please let me know if you can now access it.

@Rouben Rostamian  Sorry, I have tried the upload of the worksheet several times and it fails each time, so I deleted the non-working link. Is there another way I can make the worksheet available to you?

In addition I have altered the question's wording to try to clarify that the worksheet animates one river crossing path, namely the boat always heads towards its destination. I would also like to animate a least time path for crossing from the starting point to the destination, which I assume requires a functional definition of the boat's constantly changing heading.

@phil2 Your fix solves this problem.

@Thomas Richard I copied the Sievert routine from a book on bubbles by John Oprea. He was using Maple 5 or 6.

@vv Your fix works very well.

@phil2 This occurs on all worksheets when "quit" is selected in the Maple Debugger window. Below is a very simple example of this output. When "continue' is selected and the procedure completes normal execution only a blank text entry area is added to the worksheet.


restart; with(plots)

A := proc (Rad, a, b) DEBUG(1, Rad, a, b); plot3d([Rad*cos(theta)*sin(phi), Rad*sin(theta)*sin(phi), Rad*cos(phi)], theta = 0 .. Pi, phi = 0 .. 2*Pi, scaling = constrained) end proc:

A(1, 2, 3);

Warning,  computation interrupted



   2   plot3d([Rad*cos(theta)*sin(phi), Rad*sin(theta)*sin(phi), Rad*cos(phi)],theta = 0 .. Pi,phi = 0 .. 2*Pi,scaling = constrained)



Download DEBUG_example.mw

@Kitonum It seems your method is more general in that the conditions within the map clause can be any that the programmer desires e.g. the cap could have an elliptical shape.

@Rouben Rostamian  Thanks, your procedure will help me in my current project. I believe my azimuth and polar are equivalent to your longitude and colatitude.

@vv Thanks to you my Maple education continues.

@vv Your programming here is amazing!

Unfamiliar with recursion, I can't see how Apollo ends. In particular how can the final display command execute apparently without the preceding gen(1,2,3,4) command executing for the second time?

@Carl Love Calling a Mobius strip single-edged reveals my almost total lack of knowledge of topology. The Catalan surface seemed different because it has two cusp-like edges between curved portions of the surface.

Thanks to you, I looked up the definition of homeomorphic in Wikipedia and am now just slightly less naive with topology!

@Kitonum This is good information. Thank you.

@vv Thank you!

Setting one of the two surface variables, beta, to its constant range limits, as you did above, displays a spacecurve on the surface's curved edge.

Repeating p2 with alpha set to its constant range limits displays the surface's horizontal straight line edges.

What criteria determine which surface variable in the spacecurve will display the curved edge?

What is displayed when your technique is applied to a single edge minimal surface such as a Mobius strip?

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