The EXTRA SQUARE explained...
The EXTRA SQUARE explained...
On Pages 55/56 of
Murderous Maths: Guaranteed to Mash Your MindProfessor Fiendish sets this diabolical puzzle:
Get a square bit of paper and divide it into 8x8 squares. Mark on these lines as shown:
What is the area of this shape? It's 8x8 = 64 squares.
Now you cut along the lines to make four separate shapes.
Put your shapes together to make this rectangle:
Seems fine doesn't it? But when you work out the area you find it measures
13 x 5 = 65 squares.
Where did the extra square come from?
You'll find that if you cut the pieces out really carefully and then put them together, you can't quite get them to meet in the middle. In fact you produce a pattern looking like this:
The red bit is exaggerated, but in fact the space in the middle has the
area of 1 square. It's so long and thin that it's hardly noticable, but it's there all
the same!
