[Search for users] [Overall Top Noters] [List of all Conferences] [Download this site]

Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1159.0. "The Opaque Cube problem." by DWOVAX::YOUNG (History punishes the late - MG) Sat Dec 09 1989 21:15

    From Martin Gardner:
    
    	What is the minimal area of a set of points within a unit cube that
    will block all light paths passing through that cube?
    
    --  Barry
T.RTitleUserPersonal
Name
DateLines
1159.1AITG::DERAMOJe kunt mij toch geen poets bakken.Sat Dec 09 1989 22:283
        Well, it is less than or equal to five.
        
        Dan
1159.2HPSTEK::XIAIn my beginning is my end.Sun Dec 10 1989 16:5611
    If you dark all the points of rational coordinates on the surfaces, the 
    area is 0.  On the other hand, I don't think this is what the author of
    .0 wanted. :-)
    
    Eugene
    P.S.  As a matter of fact, I think this will do the job since lights
    are esstially continuous waves, and if you set any continuous function
    0 at the rational points, you get the 0 function.  Now if you
    model light as composed of photons of 0 surface area..., that is
    another story. :-)
                                                    
1159.3DWOVAX::YOUNGHistory punishes the late - MGSun Dec 10 1989 20:328
    Tsk, tsk.  Its a math problem, not a physics problem.  The author of .0
    intends that light be taken to be Lines in Euclidian Cubic Geometry.
    
    The set of all rational points on the surface of the cube *would* have
    area of 0, but it would also only block out 0% of all the possible
    light  paths through the cube, where light paths are idealized lines.
    
    --  Barry
1159.4Plateau's problem ?ALLVAX::ROTHIf you plant ice you'll harvest windMon Dec 11 1989 08:1021
    If you dipped it in soap film one of the possible minimal surfaces
    would do it I think...

    For example, 12 isosceles triangles from each edge to the center
    have areas summing to

	12 * sqrt(2)/4 = 3 * sqrt(2) ~= 4.24264

    Think of the analogy with the square in the plane.

	+-------+
	|\     /|
	| \   / |
	|  \ /  |
	|   X   |	<--- astigmatic square
	|  / \  |
	| /   \ |
	|/     \|
	+-------+

    - Jim