Can you say what angle is made by the two red lines drawn on two sides of the cube as shown in the illustration?

(In reply to you people have to think 3-D by mike)

"The angle isn't necessarily 60 degrees if you're thinking in terms of 3-D...there's no way it can be an equilateral triangle on the corners of a cube since the beginning points of both lines are further in distance than the red lines themselves so there's no way it's an equilateral triangle if you actually count the fact that the lines are each against a different plane. The answer is 90 degrees since each line makes a 45-45-90 triangle within each face of the cube...add them together to get 90. "

You would be correct IF the cube were made of cardboard, and we cut out those two sides, and unfolded them to make a 2 by 1 rectangle.  (assuming it's a unit cube).  Then the bottom edge would be the third leg of the triangle of sides:   sqrt(2), sqrt(2), and 2.

But imagine the cube made of wood; cut along the red line with a saw.  Put the freshly cut surface of wood on a table top.  We now have a pyramid whose base is an equilateral triangle sqrt(2) on each side.   In the plane of the cut surface, it's 60-60-60.

Posted by Larry on 2004-08-04 18:39:12