posted on Nov, 13 2004 @ 06:13 AM
Its because the top shape is not a triangle but a tetrahedron. The two triangles do not have the same proportions. So the first image may appear as a
triangle, but is in fact a tetrahedron.
When you do a little calculation (let's say the grid-unit is centimeters), the tetrahedron (the real thing) obtain the area of :
5 cm * 2 cm * 0,5 + 8 cm * 3 cm * 0,5 + 7 cm2 + 8 cm2 = 32 cm2
and below the octahedron obtain exactly the same area; the hole is just a way of explaining the illusion.
the dark-green triangle partition (rectangular), has an angle of : arctan (0,40) = 21,801°
the red triangle partition (also rectangular), has an angle of : arctan (0,375) = 20,556°
We hereby conclude that the intersection between the dark-green and the red triangle, is not a straight line, but two lines, presented with an outside
angle of 181,245° - and this appears as one line.
Its a common computer science/math problem.
[edit on 11/13/2004 by just_a_pilot]