What's wrong with geometry?

Question

What's wrong with the puzzle in this video?

I didn't understand. Do you understand what happens?

(Click the image to open the video)

Just an optical illusion as the "squares" down the middle are not true squares. The sum of the areas of the 4 parts is still 64. — SMS von der Tann, Aug 09 '16 at 17:12

score 7 · Accepted Answer · edited Mar 11 '17 at 22:54

Obviously, $64\neq65$. Observe the diagram below:

The slopes of the diagonals of the blue and pink pieces are each $2/5 = 0.4$, whereas the slopes of the diagonals of the green and red pieces are each $3/8 = 0.375$. Thus, while the shapes made by the top two and bottom two pieces may look like triangles, they are in fact concave quadrilaterals, which creates a thin white space between the pieces. This white space has area $1$, so the area, as expected, stays constant at $64$.

What's wrong with geometry?

1 Answers1