William Fish

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14 years, 100 days

MaplePrimes Activity


These are replies submitted by William Fish

Alajandro,

I know nothing beyond what is at the OLPC website.  The one I have was obtained via the Give 1 Get 1 Program (G1G1).  Some folks seem to have figured out how to make that a bad thing and so the G1G1 program may have been discontinued.  Human ingenuity, too often, has a dark side.

It works!  My worksheet works!  I am astonished [filled with sudden wonder or amazement].  I hope that's OK.

I continue to be amazed at what happens when I ask stupid questions here.  It is completely beyond my ability to predict.

Thank you all.

Here is my worksheet:

View 4937_Page147million.mw on MapleNet or Download 4937_Page147million.mw
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WARNING: I went nuts and computed a million digits so it runs for 48 minutes on my humble machine.

Thank you.  I'm reading it.

No, I did not have Gravitation but I do now.  Thank you.

This seems to be about as good as it gets:

View 4937_Page92b.mw on MapleNet or Download 4937_Page92b.mw
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It's Robert Israel's method.

I tried assuming x is between 0 and 20.  I tried making assumtions about a, b & c.  None of this helped.  Assuming positive worked wonders.  What exactly was assumed to be positive?  Assuming real seemed to have the same affect as assuming positive.

evalc(...) assuming positive;

worked like magic (Arthur C. Clarke's 3rd law).

I read Maple Int/int error?  CASs are complex and imperfect.

View 4937_Page92a.mw on MapleNet or Download 4937_Page92a.mw
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Robert,

As you know, I tried

assume(-b <= y, y <= b, c <= z, z <= a+c)

and it didn't help.  Is this because it gives Maple no new information because the definite integrals already provided this information?

assuming positive

worked wonders.  I tried this too

assuming real,positive

and it seemed to do good things also.  Here is a worksheet:

View 4937_Page92JohnFredsted.mw on MapleNet or Download 4937_Page92JohnFredsted.mw
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Can you help me understand what assuming does here?

Here is a quote from page 92 and 93 of When Least Is Best by Paul J. Nahin:

"...set the derivative...equal to zero and solve...proves to be an astonishingly ugly business!"

Robert Israel,

Here is Nahin's answer:

arcsin(((b^2-x^2)*(x^2+(a+c)^2)-2*x^2*b^2)/((b^2+x^2)*(x^2+(a+c)^2)))-arcsin(((b^2-x^2)*(x^2+c^2)-2*x^2*b^2)/((b^2+x^2)*(x^2+c^2)))

As far as I can tell, your answer is the same as Nahin's.  Nahin says "a good table of integrals is the "method" I used!".  Your method is clear.  I can follow it.  Someday I like to think that I will be able to do it.  You have no idea how entertaining I find your mathematics.  Thank you.

Here is my worksheet:

View 4937_Page92RobertIsrael.mw on MapleNet or Download 4937_Page92RobertIsrael.mw
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That worked.  Thank you.

I like the way you did the plotting.  I'll try to add that to my inventory.

View 4937_page85.mw on MapleNet or Download 4937_page85.mw
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I just tried that and extrema returned {0}.

Zsolt,

Thank you.  That's it.  Thanks again.

View 4937_page84.mw on MapleNet or Download 4937_page84.mw
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Joe,

Thanks.  That's the first Maple animation that I've seen.

View 4937_page27.mw on MapleNet or Download 4937_page27.mw
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Does anybody know why there was a problem downloading the worksheet?  When I tried the download worked.  I'd like to try to avoid that problem in the future.

View 4937_page27.mw on MapleNet or Download 4937_page27.mw
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I hope you can see the above worksheet.  I've converted to your way.  Now if I can just start thinking like you.  Thank you very much.

View 4937_page27.mw on MapleNet or Download 4937_page27.mw
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I had a space in the file name.  I wonder if that could be the problem.  I took it out.

I like compact above.

Here is a fragment of the worksheet that you couldn't get:

> plot([T(1, theta), T(2, theta), T(3, theta), T(4, theta), T(5, theta)], theta = 0 .. Pi);

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