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September 26, 2017, 06:28:55 PM
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: Geometry revisited!  ( 3823 )
« : August 24, 2007, 01:22:13 PM From Prateek»



Geometry revisited!


What is the size of the largest square that will fit in the unit cube?

 
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« #1 : August 24, 2007, 07:25:41 PM From PSM»

is it the side of the square 2^.5 ?????
reply plzzz
« #2 : August 25, 2007, 09:33:28 PM From Prateek»

No PSM, the size of the square is larger than one face of the cube. By the way, I didn't get your formula!
« #3 : August 26, 2007, 11:19:38 AM From PSM»

ya ya thts wht i'm telllin..........
side of the cube is 1 okk x=y=z=1
from it one side of the square is sqrt 2
sqrt=squareroot of 2
or side of the sqaure is 1.414
area is 1.414*1.414 = 2
« #4 : September 21, 2007, 12:25:30 PM From Rajesh»

largest side of square = sqrt(9/8) = 3/[2*sqrt2] units..

let 'O' be the origin..A(1,0,0), B(1,1,0), C(0,1,0), O'(0,0,1),A'(1,0,1), B'(1,1,1), C'(0,1,1) now take points
P(3/4,0,0) on OA
Q(0,3/4,0) on OC
R(1/4,1,1) on C'B'
S(1,1/4,1) on A'B'
now for the square PQRS u can check
PQ=QR=RS=SP=3/[2*sqrt2]
and also from vector or 3-D check that
PQ is perpendicular to QR and PS
and RS is perpendicular to PS and QR.

so the side PQ = sqrt(9/8) units
and area of that square = 9/8 sqr unit


what u say prateek....
« #5 : September 26, 2007, 04:52:35 PM From vishwakarma.deepak»

nice work rajesh....but its quite near to 1 unit...

guyz, Is there any other optimized square possible in unit cube...
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