[BlindMath] Tactile Pythagoras

[Jonathan Fine]

Happy New Year!

Here's a puzzle, whose solution provides the geometric part of the proof of
the Pythagoras theorem. The reasoning part will follow later. Recall that 3
squared plus 4 squared equals 9 plus 16 equals 25 equals 5 squared.

You're given seven tiles. They are
a) Three squares with side lengths 3, 4 and 5 (and thus areas 9, 16 and 25).
b) Four identical right angled triangles, all with side lengths (3, 4, 5).
Each triangle has area 6.

The puzzle has two parts. The first part is to cover exactly a 7 by 7
square using all but one of the tiles you've been given. The second part is
to do the same, but using all but two of the tiles.

Hint: Note that 7 is 4 plus 3. The total area of the triangles is 24. Note
that 24 plus 9 plus 16 is 49, which is 7 squared. Note also that 24 plus 25
is also equal to 7 squared. This tells you which tiles are not used in the
two parts of the puzzle.

By all means discuss this puzzle on the list, but I'd prefer that there
were no spoilers. Contact me off list if you wish. I'll give the solution
to the puzzle later this week. Providing a PDF for a tactile image printer
or a sighted assistant is on my TODO list.

I've learnt a lot from most useful conversations with Abdulqadir, Dana,
Fawaz, Janet and Jonathan G. regarding this puzzle. I'm most grateful to
them, and to this list for providing a place to share.

with kind regards

Jonathan