New balls have seams that are more contiguous --> cheaper production The seams have a similar importance for soccer balls as the dimples for golf balls. At high speed local turbulences at the seams lead to a laminar air flow of the whole ball. Goalkeepers hated the ball of the world championship 2006 because of large areas without seams. As already mentioned by Dave: At certain speed (transition from laminar to turbulent air flow) the behaviour of a ball (which does not rotate) is unstable. Walter
-----Ursprüngliche Nachricht----- Von: math-fun [mailto:math-fun-bounces@mailman.xmission.com] Im Auftrag von math-fun-request@mailman.xmission.com Gesendet: Samstag, 14. Juni 2014 20:35 An: math-fun@mailman.xmission.com Betreff: math-fun Digest, Vol 136, Issue 27
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Today's Topics:
1. Re: Soccer balls (Dan Asimov) 2. Re: Soccer balls (Dave Dyer) 3. Re: Soccer balls (Dave Dyer) 4. Re: Soccer balls (Dan Asimov) 5. earth has vast internal water reservoir? (Warren D Smith) 6. Re: Close enough for Government work (Bill Gosper) 7. Trying to locate Marc Paulhus (Neil Sloane)
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Message: 1 Date: Fri, 13 Jun 2014 10:13:04 -0700 From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Soccer balls Message-ID: <CE6EA8C8-5FD8-4256-A1C6-AE56A837E9BB@earthlink.net> Content-Type: text/plain; charset=us-ascii
The sense I get from various web pages is that some felt it was too easy to kick a seam and get unpredictable behavior from the ball. It's not clear how the new design (as well described on the first page of the site below) avoids this. (Six propeller-shaped panels each with 4-fold chiral symmetry, fitting together like the faces of a cube.)
I think the improvement isn't just in the geometry of the panels, but also in the way the seams are sealed, making the seams a smaller fraction of the total surface area.
--Dan
On Jun 13, 2014, at 12:11 AM, Stuart Anderson <stuart.errol.anderson@gmail.com> wrote:
Not being a big soccer fan, not across the latest on the design, authorised use and reasons for the shape and construction of soccer balls. Looking at the opening game I noticed the truncated icosahedron ball is no longer in use. I found this article which compares the properties of different shaped balls http://www.nature.com/srep/2014/140529/srep05068/full/srep05068.html Does anyone know why the truncated icosahedron is no longer used in the World Cup?
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Message: 2 Date: Fri, 13 Jun 2014 10:51:31 -0700 From: Dave Dyer <ddyer@real-me.net> To: math-fun <math-fun@mailman.xmission.com>, math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Soccer balls Message-ID: <E1WvVeM-0002NF-Ct@mx02.mta.xmission.com> Content-Type: text/plain; charset="us-ascii"
New scientist has had several articles on this, both current and back when the old ball was introduced. The gist I got was that the seam pattern influences the point at which the ball becomes unstable as it loses velocity and spin.
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Message: 3 Date: Fri, 13 Jun 2014 10:51:31 -0700 From: Dave Dyer <ddyer@real-me.net> To: math-fun <math-fun@mailman.xmission.com>, math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Soccer balls Message-ID: <E1WvVeM-0002NG-BA@mx02.mta.xmission.com> Content-Type: text/plain; charset="us-ascii"
New scientist has had several articles on this, both current and back when the old ball was introduced. The gist I got was that the seam pattern influences the point at which the ball becomes unstable as it loses velocity and spin.
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Message: 4 Date: Fri, 13 Jun 2014 11:32:15 -0700 From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Soccer balls Message-ID: <8FF1C15E-F1DC-4FE9-81D3-406520178CD7@earthlink.net> Content-Type: text/plain; charset=us-ascii
This non-article in the NY Times gives a nice exploded view of the three large balls depicted, at least if you click on them.
Warning: This does not work on my iMac with Mavericks when I use Firefox, butg works with Safari.
--Dan
On Jun 13, 2014, at 10:51 AM, Dave Dyer <ddyer@real-me.net> wrote:
New scientist has had several articles on this, both
current and back
when the old ball was introduced. The gist I got was that the seam pattern influences the point at which the ball becomes unstable as it loses velocity and spin.
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Message: 5 Date: Sat, 14 Jun 2014 00:58:04 -0400 From: Warren D Smith <warren.wds@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] earth has vast internal water reservoir? Message-ID:
<CAAJP7Y3R4cYE-FEtFuG+R9B9=OVvidLw3ugj9yAjRzjWzyrrLQ@mail.gmail.com> Content-Type: text/plain; charset=ISO-8859-1
http://www.cbc.ca/news/technology/deep-earth-has-oceans-worth- of-water-10-diamond-reveals-1.2569564
From tiny observations follow huge conclusions: Somebody found a diamond containing a mineral inclusion, said mineral 1.5% water. This"proves" there is a tremendous amount of water in Earth mantle diamond forming region, from which we extrapolate this region contains way more water than all oceans. This in turn suggests a geologic water cycle where ocean water subducted into the mantle, and outgassed from same... this is rather revolutionary change in view...
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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Message: 6 Date: Sat, 14 Jun 2014 04:49:17 -0700 From: Bill Gosper <billgosper@gmail.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] Close enough for Government work Message-ID:
<CAA-4O0F-ERNPLvS5TnuHegEU2u7B94-J7XHjUSwPen-Te+fdCg@mail.gmail.com> Content-Type: text/plain; charset=UTF-8
On Mon, Jun 9, 2014 at 7:36 PM, Bill Gosper <billgosper@gmail.com> wrote:
Ideally, we might find formulas for a(x), c(x), d(x), and q(x). (I keep providing for b(x), but it always comes out identically 1. ?)
On Mon, Jun 9, 2014 at 4:30 AM, Bill Gosper <billgosper@gmail.com> wrote:
Rejected but juicy http://arxiv.org/abs/math/0703470 (p 9) describes the remarkable (to me, anyway) *polynomial* valued Somos4
s[0] = 0; s[1] = s[2] = 1; s[3] = -1; s[4] = x; s[n_Integer /; n > 4] := Factor[(s[n - 1]*s[n - 3] + s[n - 2]^2)/s[n - 4]]
In[536]:= s /@ Range[12]
Out[536]= {1, 1, -1, x, 1 + x, -1 - x + x^2, -1 - x - x^3, -x (2 + 3 x), 1 + 3 x + 3 x^2 - x^4 + x^5, -(1 + x) (-1 - 2 x + 2 x^2 + 3 x^3 - x^4 + x^5), -1 - 3 x - 3 x^2 - 5 x^3 - 9 x^4 - 3 x^5 + 2 x^6 - x^7, -x (-1 - x + x^2) (3 + 9 x + 9 x^2 + 5 x^3 + 2 x^4 + x^6)}
[Clipped: four variable relations] The polynomial degree goes up like n^2/16 plus a period 8 ripple.
For x:=1, s[n] can be expressed in "closed form": a*c^n^2*EllipticTheta[1, d*n, q]: (0.31749282989638009698851538146011901061695 + 0.41577568158982458340525424882529254242763 I) (0.74320667986312908167383113199924669418636 - 0.69294655945321371719182977376188612597500 I)^n^2
EllipticTheta[
1, (1.7554385915026838183474896476936322715588657 + 0.050402131298346764198930943819803546234487011 I) n, -0.43035475675354998492420504350604355525329714 - 0.63418111840450730747740547053917541440014778 I]
Table[%, {n, -4, 13}] // Chop
{-1.000000000000000000000000000000000000000, 1.0000000000000000000000000000000000000000, -1.0000000000000000000000000000000000000000, -1.0000000000000000000000000000000000000000, 0, 1.0000000000000000000000000000000000000000, 1.0000000000000000000000000000000000000000, -1.0000000000000000000000000000000000000000, 1.000000000000000000000000000000000000000, 2.00000000000000000000000000000000000000, -1.000000000000000000000000000000000000000, -3.00000000000000000000000000000000000000, -5.00000000000000000000000000000000000000, 7.0000000000000000000000000000000000000, -4.0000000000000000000000000000000000000, -23.000000000000000000000000000000000000, ...}
(Find *those* a,c,d,q in ISC.) The paper suggests that there are several other such expressions for s[n]. It will be interesting to see how a, c, d, and q vary with x. --rwg
[Clipped: Numeric difficulties.]
For x = -2/3, we get a slightly messy but exact closed form 3^(1/16 (-n^2 + (5 + (-1)^n - 2 Sqrt[2] Cos[(n ?)/4] + 4 Cos[(n ?)/2])^2 Sin[(n ?)/4]^4)) (4 Cos[(n ?)/ 8] Cos[(n ?)/4] - (-1)^n (Sqrt[2] + (-2 + Sqrt[2]) Cos[(n ?)/4]) Cos[(n ?)/ 2]) Sin[(n ?)/8]
(no ?, no mysterious q), but 0,1,1,-1,-2/3,1/3,1/3^2,-1/3^3,0,1/3^5,-1/3^6,-1/3^7,2/3^9,1/3^10,... is no longer a Somos sequence! The problem is that s[8n] is a multiple of 3x+2, and there's no way to continue the recurrence more than three steps past those periodic 0s.
The paper's "closed form" had an eight way case statement.
There is also an exact ? expression ((-1)^(1/8) Sqrt[2] EllipticTheta[2, 0, I q])/(3^(1/4) EllipticTheta[2, 0, q])
where q ->Root[{-((1 + I)/3^(1/4)) + ( QPochhammer[-1, #1^2] QPochhammer[-(1/#1^2), #1^4])/( 2 (1 + 1/#1^2)) &, 0.591308037470 + 0.442317013236 I}]
specifying q, and thus the ? quotient, to arbitrary precision, but with no hint the values are rational, or even real. Interestingly, the problematic (0/0) values of the recurrence are s[8n+4], whereat the ? quotient is conveniently independent of q.
The paper mentions finding q -> Root[{Product[(1 + #^(2*k))*(1 + #^(4*k - 2)), {k, \[Infinity]}] - (1 + I)/ 3^(1/4) &, .7241830710727415040344246937315* I + .5068861260317593704061905537186}] producing a puzzling algebraic sequence, but Root can't pick up the scent.
More generally, if there is some algebraic x for which s[n] vanishes, then it will periodically vanish for s[k n], and there will be a messy (non-?) closed form, as above. --rwg
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Message: 7 Date: Sat, 14 Jun 2014 14:34:33 -0400 From: Neil Sloane <njasloane@gmail.com> To: fun <math-fun@mailman.xmission.com> Subject: [math-fun] Trying to locate Marc Paulhus Message-ID:
<CAAOnSgSE5VZst9JbHiYPV_-29PhH5usbcNSy76caj+RfQE=Tmw@mail.gmail.com> Content-Type: text/plain; charset=UTF-8
There are several references in the OEIS to a preprint:
Marc Paulhus (paulhus(AT)wanadoo.nl), Pikelets, Discrete Math., (but apparently unpublished).
I am trying to get hold of the article - can anyone help?
Or, can anyone give me his email address? The one I have is broken.
He has worked with Richard Guy and others on game theory: For example: Dan Calistrate, Marc Paulhus and David Wolfe, On the lattice structure of finite games, in More Games of No Chance (Berkeley, CA, 2000), Math. Sci. Res. Inst. Publ., 42, Cambridge Univ. Press, Cambridge, 2002, pp. 25-30.
Thanks Neil
-- Dear Friends, I have now retired from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
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