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MaplePrimes Activity

These are replies submitted by Earl

@Kitonum Thank you for showing me the ODE technique and how to code an animation of a procedure.

@Kitonum I appreciate the beauty in Rouben Rostamian's answer, however I have chosen yours as the best answer because you have shown me an important technique of which I was unaware. Thanks again! 

@Rouben Rostamian  What a lovely display! Especially the shading produced when the two colors overlap. Thank you greatly!

@Kitonum I have tried many ways to apply your technique to the website's last equation containing differentials and cannot produce a differential equation, which, when solved, yields the slope lines portrayed in the website's accompanying diagram.

How can y*cos(x)*dy -sin(x)*dx be converted to a solvable differential equation?

@Kitonum I am grateful to you for this lesson. After studying its implications I will try to apply it to several of such equations in the cited website

@Carl Love My searches will benefit from your advice.

@Rouben Rostamian  You have given me two gifts! First, I will carefully study your answer and try to absorb this lovely technique.

Secondly, you have opened up a new field of exploration for me as I attempt to apply this to a variety of other interesting surfaces.

You likely already are aware of the almost endless variety of these on https://mathcurve.com/surfaces.gb/surfaces.shtml 

@dharr Thanks for the complement. Maple's VectorCalculus has a TangentPlane command and I was aware of the verbal description of a pedal surface, but my math skills are not up to using this information to form a general definition. Hopefully I'll know more after examining Rouben Rostamian's answer above.

@Carl Love Thank you for this information. I posed this question of the forum after searching the internet as you did (without the quotes) and finding nothing beyond Wikipedia's "Pedal curve"

@Kitonum My wife found the oloid hard to visualize. Your animation will help her.

I'm intrigued. What other 3D shapes would you describe as "outlandish"?

@Rouben Rostamian  I greatly appreciate the educational aspect of this and many of your previous replies. In future, I will look for alternate and simpler parametrizations of surfaces. Thank you.

@acer I tried the option grid = [100,100] but it didn't affect the plot's smoothness. It seems I used the wrong grid values.

@vv I thank you for your  excellent reply.

Is there any way in which the "distorted" grid indicates the complex expression in F(x,y) or can this only be found by trial and error?

@vv Thank you for your reference. I will pursue it and its sub-references and hope to expand my knowledge.

@dharr I hope in future to have additional questions sufficiently intriguing to draw your interest.

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