150. - DISSECTING A MITRE

150. - DISSECTING A MITRE

From "Amusements in Mathematics" by Henry Ernest Dudeney (first published
1917).

http://www.puzzles.50webs.org/pics/q150a.png

The figure that is perplexing the carpenter in the illustration represents
a mitre. It will be seen that its proportions are those of a square with
one quarter removed. The puzzle is to cut it into five pieces that will
fit together and form a perfect square. I show an attempt, published in
America, to perform the feat in four pieces, based on what is known as the
"step principle," but it is a fallacy.

Dudeney then goes on then to explain how a suggested four-piece solution
is not actually valid. In the context that was important, but presents
something of a distraction. We are looking for a five piece solution. You
can read the whole discussion at the link below:

http://www.puzzles.50webs.org/various_dissection.html

Describing any solution in a text based medium will be a challenge, but if
you are happy to take on the puzzle and mark your own work that's good
enough for me.

Good luck,
--
David Entwistle