From: rusin@washington.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: Q: Baseball
Date: 1 Aug 1995 05:27:35 GMT
In article , Hein Hundal wrote:
>Does anyone know an equation for the seam of a baseball? Based on some
>measurements, I have made the following guess for one peice layed flat:
>
>x[t] = -1.3 Cos[Pi t/4] -.0236 Cos[Pi 3 t/4]
>y[t] = .408 Sin[Pi t/4] +.158 Sin[Pi 3 t/4]
>
>0 <= t <= 8.
>
>(Two such pieces almost make a diameter 1 sphere. Of course, no two flat
> peices of material can exactly cover a sphere.)
I don't know in what shape the pieces are really cut but I question the
accuracy of your curve. The area of a region of the plane whose boundary
is given parametrically is the integral of the one-form y dx, that is,
the integral of y(t)*x'(t) (in your case from t=0 to t=8). I
compute the area of each piece to be 1.70144 in this way. This gives a
total area of 3.40288, which is not impressively close to the true
surface area 4 pi (1/2)^2 = pi = 3.14159... of the sphere. It might be
reasonable to work back from this information and adjust the four constants
to get a closer area approximation, but I'd have to say it strikes me as
more appropriate simply to report your coefficients with fewer decimal
digits of accuracy.
(Of course as you noted the resulting figure is not really a sphere
anyway, so it is perhaps unreasonable to ask that the area really be pi.
Still, I found it odd to see so many digits included.)
dave