Re: How to Make Cisterns

On 03/05/2025 09:08, David Entwistle wrote:

Adapted from "Amusements in Mathematics" by Henry Ernest Dudeney.
 Given a large sheet of zinc, measuring (before cutting) one metre square,
you are asked to cut out square pieces (all of the same size) from the
four corners of this sheet. You are then to fold up the sides of the
resulting shape, solder the edges and make a cistern. The cistern is open
at the top. You can assume you have the appropriate tools and skill to
carry out the task.
 The puzzle is what size should the cut out pieces be, such that the
cistern will hold the greatest possible quantity of water?

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Side = 999999 microns, volume = 698521279 cubic microns.
Side = 999997 microns, volume = 791833765 cubic microns.
Side = 999995 microns, volume = 909146179 cubic microns.
Side = 999993 microns, volume = 1050458473 cubic microns.
Side = 999991 microns, volume = 1215770599 cubic microns.
Side = 999989 microns, volume = 1405082509 cubic microns.
Side = 999987 microns, volume = 1618394155 cubic microns.
Side = 999985 microns, volume = 1855705489 cubic microns.
Side = 999983 microns, volume = 2117016463 cubic microns.
Side = 999819 microns, volume = 2131502515 cubic microns.
Side = 998659 microns, volume = 2137812763 cubic microns.
Side = 998374 microns, volume = 2144275288 cubic microns.
Side = 997379 microns, volume = 2145052699 cubic microns.
Side = 995252 microns, volume = 2147110208 cubic microns.
Side = 930405 microns, volume = 2147409565 cubic microns.
Side = 925780 microns, volume = 2147420992 cubic microns.
Side = 912006 microns, volume = 2147446488 cubic microns.
Side = 777683 microns, volume = 2147468811 cubic microns.
Side = 461441 microns, volume = 2147475329 cubic microns.
Side = 357737 microns, volume = 2147481849 cubic microns.
The last entry is of course the winner.

I guess a follow on question could be; is it possible to cut out four non-
square pieces (all of the same size and shape), producing a cistern with
tapering sides, which has greater volume. I haven't looked at that yet...

"Easily" was my immediate reaction... but then I thought about it, and decided that it... well, that it's a far better question than it looks. :-)
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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