64 = 65? Still Not Convinced? But this can not be true what is the ...

Answer:
Ok, the 8x8 figure is correct. The right figure (the red one) is built on three consecutive
Fibonacci numbers, but they can figure what is wrong with it by using the Pythagorean
Theorem.
First, if they cut and rearrange this small figure they will not discover that anything is
wrong as one area unit is so small. So that is a red herring.
Now to the solution,
Calculate how long the diagonal should be in the right figure (the red one):
2 2
Diagonal: 13 + 5 = 13.92839
Next calculate the length of the sides of the two figures on the bottom (the triangle and
the top of the trapezoid).
2 2
Triangle: 8 + 3 = 8.544004
Trapezoid:
2 2
5 + 2 = 5.385165
Sum: 13.92917
So the sum of the length of the two figures is slightly longer than the diagonal.
Conclusion: When rearranging there is not a straight line corner to corner, the line is
bowing slightly inward which creates that extra square between the figures along the
diagonal.