Re: [Phys-L] playing for keeps

[Robert Cohen <Robert.Cohen@po-box.esu.edu>]

FWIW, it might be easier to see the pattern when written in terms of diameter:

Perimeter of square = 4*D
Area of square = D^2

Perimeter of circle = pi*D
Area of circle = pi*D^2/4

Surface area of cube = 6*D^2
Volume of cube = D^3

Surface area of sphere = pi*D^2
Volume of sphere = pi*D^3/6

Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@esu.edu    http://www.esu.edu/~bbq 


-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Bruce Sherwood
Sent: Saturday, June 29, 2013 9:46 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] playing for keeps

Good point, John M. (Are half of the people on this list named John?) So here's a more complete summary.

Bounding square/circle:
   perimeter 8r/2pi*r = 4/pi = 1.27
   area 4r^2/pi*r^2 = 4/pi = 1.27 (odd that the ratios are the same)

Bounding cube/sphere
   area 24r^2/4*pi*r^2 = 6/pi = 1.91
   volume  8r^3/(4/3)pi*r^3 = 6/pi = 1.91

Seems like it ought to be easy to see why these pairs work....??

Bruce


On Sat, Jun 29, 2013 at 6:09 PM, John Mallinckrodt <ajm@csupomona.edu>wrote:

> Bruce,
>
> You left out the area of the bounding cube/area of sphere which also 
> equals 6/pi.  Bet we can find a "reason" for those two apparent 
> coincidences!
>
> John Mallinckrodt
> Cal Poly Pomona
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