Thread: Crazy.

Kinda like this one!

Here are a few more:

Hmmm...I don't need math to prove to me that girls are evil...

well since the basic topic of this post is optical illusions, we know that there has to be some sort of illuision going on here. empty space just doesnt appear. so here is how this illusion works:

basically, the top one is dented down, and the bottom one is bubbled up, but just slightly enough for you not to notice without careful investigation.

more detailed explaination:
if you look at the intersection between the red triangle and the dark green triangle on the upper layout, you will notice that they intersect exactly at the grid lines. then if you follow that same grid line down, you will see that the red triangle (after being moved) has a hypotenuse that is above the grid line intersection.

likewise if you look at the intersection of the two triangles after they are rearranged, you will see that they touch at the grid line intersection also, but following that line up to the original picture, the red triangle is below that same grid line intersection.

basically, what is happening here is that if you drew a line connecting the upper right corner and the lower left corner of the triangle, which would show you the true hypotenuse, you will see that the line is above the "hypotenuse" drawn in the upper diagram. and if you do the same on the bottom diagram you will see that the true hypotenuse lies below the "hypotenuse" that they have shown you.

from a mathematical standpoint, the area between the true and "as-drawn" hypotenuses on the upper digagram should be 1/2 of a square unit from the grid. and likewise on the bottom diagram, the diference between the two hypotenuses should be 1/2 of a square unit. if you add up the "missing" 1/2 from the upper drawing, and the "extra" 1/2 from the bottom drawing, you should get the 1 square unit hole in the second diagram.

hope it makes sense!!!

~mike