Transcript Slide 1

If I were to show you this
tiling pattern I doubt that
you would think it had
anything to do with
Pythagoras’ theorem.
However on further
investigation we can see how
it was constructed.
This is a small section of the grid
and when we use different
colours to fill it in it starts to
make more sense.
In the figure below, the blue square is the
square of the hypotenuse of the red
triangle. The blue square is clearly equal in
area to the purple plus the green square. But
the purple square is the square of one of the
legs of the red triangle. The green square is
the square of the other leg. This dissection is
attributed to Henry Perigal.
You can create your own Pythagorean
tiling pattern. Firstly;
Start with any right
triangle
Add the square on the
hypoteneuse
Add the square on one side
Extend the sides to start
the grid
Now the
pattern has
been
established
repeat it:
The red and yellow
squares are the squares
on the legs. These 2
squares can be cut up
and reassembled into a
square that is the same
size as the square on the
hypotenuse. This
dissection was devised
by Thabit ibn Qurra
around 900 A.D.