(In reply to re: Where To Place The Square
Viewed from above, one slanted edge of the tilted square cuts off on the base of the cube the hypotenuse of a right triangle that is 1/4, 1/4 and sqrt(2)/4, that last being the hypotenuse, and the length of the projection of a side of the square onto the base. Since the top of the side is on the top of the cube, it is 1 unit up. The angle that the side (and therefore the plane of the square) makes with the vertical is therefore arcsin(sqrt(2)/4) = 20.7048... degrees, making the square have an angle of 69.295... degrees with the horizontal base.
The angle of an edge of the square with a vertical face of the cube would have a sine equal to (1/4)/sqrt(1+1/4^2), making the angle 14.036... degrees. But this is not the angle between the planes.
Posted by Charlie
on 2004-12-27 02:13:30