[math-fun] problem: intersecting annuli
Consider an annulus in Euclidean D-space with inner radius R and outer radius R+W. (If D=2 this means the region inside R+W circle and outside R circle. If D=3 then spheres not circles.) Now consider the set-intersection of D such annuli, respectively centered at the D vertices of a (D-1)-dimensional simplex. What is the AREA (if D=2, or VOLUME if D=3) of this region, as a function of R,W and the simplex? An exact formula should be attainable but complicated when D=2 and D=3. (Trivial answer 2W when D=1.) But I am interested in the LIMIT of large R and small W with simplex fixed, and in this limit there should be a fairly simple asymptotically correct inexact formula. -- Warren D. Smith http://RangeVoting.org
Mathematica puzzle: What is the shortest input string that will get Mma version 9.0 to output the following, formatted like this: Except, what I see here as many rectangles are each (on my Mac) what appears instead to be a capital W sitting on a sideways 3 (rounded side up). --Dan
Dan, maybe make a jpeg of the screenshot? I see zilch Wouter. -----Original Message----- From: Dan Asimov Sent: Sunday, December 22, 2013 9:03 AM To: math-fun Subject: [math-fun] Mathematica 9.0 puzzle Mathematica puzzle: What is the shortest input string that will get Mma version 9.0 to output the following, formatted like this: Except, what I see here as many rectangles are each (on my Mac) what appears instead to be a capital W sitting on a sideways 3 (rounded side up). --Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
And on my iMac I see empty squares together with a wild mixture of pictograms, what might be Celtic ornaments, Arabic and generally oriental-ish alphabets ... WHERE did you get that font --- where DID you get that font? WFL On 12/22/13, Wouter Meeussen <wouter.meeussen@telenet.be> wrote:
Dan,
maybe make a jpeg of the screenshot? I see zilch
Wouter.
-----Original Message----- From: Dan Asimov Sent: Sunday, December 22, 2013 9:03 AM To: math-fun Subject: [math-fun] Mathematica 9.0 puzzle
Mathematica puzzle:
What is the shortest input string that will get Mma version 9.0 to output the following, formatted like this:
Except, what I see here as many rectangles are each (on my Mac) what appears instead to be a capital W sitting on a sideways 3 (rounded side up).
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
"FL" == Fred Lunnon <fred.lunnon@gmail.com> writes:
FL> And on my iMac I see empty squares together with a wild mixture of FL> pictograms, what might be Celtic ornaments, Arabic and generally FL> oriental-ish alphabets ... FL> WHERE did you get that font --- where DID you get that font? WFL The characters in the mail were all in the UCS's Private Use section, so the appearance is dependent on what fonts the viewer has, and how the viewer's software chooses which font to use for PUA characters. My MUA picked a Bhutanese/Tibetan font for those code points. Not, I expect, what Dan intended. :^/ -JimC -- James Cloos <cloos@jhcloos.com> OpenPGP: 1024D/ED7DAEA6
participants (5)
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Dan Asimov -
Fred Lunnon -
James Cloos -
Warren D Smith -
Wouter Meeussen