Can Someone Explain This?

...before I go crazy, please. Where does this hole come from? This is not a hoax or a joke. See for yourself. There got to be an mathematic explaination somehow.

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]

That was an excellent formula, just_a_pilot.

It's an optical illusion. If you place one triangle on top of the other one , they are not the same shape. It's a good brainteaser though.

Wow, thanks just_a_pilot.
I didn�t expect to get an answer like this. And so quickly as well.
Well done

Its a problem I present to programmers when I interview them for a job at work.