Reply #17: The hole has nothing to do with the triangles. [View All]

[kentauros]

Look at the grid, not the slopes. None of the shapes changed in any way when they were rearranged. BUT, the area that the two rectangular pieces occupied did change. The rectangular pieces also dropped down one square in order to handle the longer side of the red triangle and the short side of the teal triangle. Notice, too, that the area these two shapes cover have a common point on the hypotenuse. This is key to the area change. The difference between the two points also is key to why the hole shows up, and has to do with the difference in the area between the two points. That is, the area not used in the rectangular area change. It's anotehr triangle, so look at it and compare its area to that of the hole.

In the first triangle, the rectangular shapes occupy an area of 3x5 squares.
In the second triangle, the rectangular shapes occupy an area of 2x8 squares.

15 squares versus 16 squares, thus the hole :D


I hope I've explained that well enough...