Re: Paper puzzle

On 28/04/2025 08:55, David Entwistle wrote:

Here's an easy puzzle, if you have all the facts to hand.
 If you cut two A4 sheets of paper along the diagonal, you can arrange the
four triangular pieces into a square, with the pieces touching, but not
overlapping and the diagonals forming the outer edge of the square. There
will be a small uncovered area in the centre of this arrangement.
 What proportion of the area of the larger square does the central
uncovered square area form?

No doubt I've screwed up somewhere, but just in case I haven't here's a spoiler alert:
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If this is true for A4, it is true for all A*. All A* sheets have an aspect ratio of 1/sqrt(2). I will choose * so that the shorter side has length 1.
Pythag tells us that the diagonals are sqrt(1^2 + sqrt(2)^2), or sqrt(3).
The area of a square with sides sqrt(3) is 3.
The area of two sheets is 2 * sqrt(2), so we have a central square of area 3-(2*sqrt(2)), and thus a ratio of:
3 - (2 * sqrt(2))
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--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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