The Dissappearing Square
Question
You have the following two pictures - clearly, each is an arrangement of the pieces in the other, so from whence the hole?
Answer
In both arrangements of the pieces, it appears you have two right triangles with base = 13 units and height = 5 units. So, it seems impossible to get a hole by rearranging the pieces:
The trick is that neither the upper nor lower picture is a right triangle.
In the upper picture, the "hypotenuse" has a slight corner making it concave. In the lower picture, the "hypotenuse" bends outward making it slightly convex.
Here's an easy visual check: in the upper picture, the red and green triangles meet at a point 8 over from the left, and 3 up from the bottom. Look at the point 8 over and 3 up in the lower picture and you'll see that it is inside the figure.
Similarly, the triangles meet at 5 over from the left, 2 up from the bottom in the lower picture. In the upper picture, however, the point 5 over and 2 up is above the figure.
The lower picture bulges out more than the upper picture.
To make up for the extra area, it loses one square at the bottom.
Answer by drfreakazoid (Nov 17, 12:46 AM)