Re: Divide a shape into four equal parts

On Wed, 2 Jul 2025 02:36:29 +0000, IlanMayer wrote:

A well-known puzzle is to divide an L-shape - a square with one square
quarter removed - into four identical pieces.
>
But what about a square where the quarter removed is an isosceles
right-angled triangle with one of the sides as its hypotenuse?
>
This problem was set in Peter Parley's Annual, 1877, but I fear that
they are no longer available to provide the answer:
>
https://i.ebayimg.com/images/g/BZUAAOSwPqVlS8OY/s-l1600.jpg or
https://web.archive.org/web/20250701185837/https://i.ebayimg.com/

images/g/BZUAAOSwPqVlS8OY/s-l1600.jpg

>
-- Richard

 
SPOILER

Hi Ilyan,

I failed to find a solution after an hour or so of looking (shuffling bits
of paper), so was fascinated to see a solution.

Are we sure those shapes are identical? Two look the same, one looks to be
a reflection of the first two, and the third looks to be a different
shape. They all have the same area, but I don't think you would describe
them as the same shape.

Apologies if I have this wrong, which I may well do.

I think the problem is very much related to the second of Dudeney's
problems, which I'll post shortly.


--
David Entwistle