# [seqfan] Re: Splitting the square into equal parts

Neil Fernandez primeness at borve.org
Tue Nov 10 15:17:23 CET 2020

```Hi Jean-Luc,

In message <1168160906.43556410.1605015987552.JavaMail.zimbra at unicaen.fr
>, Jean-Luc Manguin <jean-luc.manguin at unicaen.fr> writes

>Your definition is a bit reductive ; I give a very simple example with 4 parts :
>we can cut the square in 2 halves and then cut those halves in 2 parts. But if
>we follow your definition, wa cannot do like this, and we get another set, a bit
>smaller.

Ah, I see - you are allowing cuts to cut-off pieces. My apologies: I
defined a different sequence. (It's still a nice one, though :-) .)

>Sorry but I cannot really follow your last paragraph... What do you mean by
>"starting rectangle" ? If the goal is to split the square into equal parts,
>there are only a few solutions for the size of the first rectangle...

By starting rectangle I meant the shape we start with, which in your
formulation is a square but which we might generalise to a rectangle
which is not necessarily a square. Unfortunately I was mistaken here too
because as Jack rightly points out the side length ratio doesn't affect
a(n). (Many thanks for this, Jack.)

In message <CABC07KeALWhzaP02Sshaf7-HVNNdRwFoPDxod2R84d8BcYE19Q at mail.gma
il.com>, Jack Grahl <jack.grahl at gmail.com> writes

>I may have misunderstood but it seems to me that the side length ratio
>doesn't affect the question at all?
>
>We should be able to take a solution for a square and stretch the square
>along one axis without affecting the relative areas of the rectangles, and
>the same to transform a rectangle into a square.

Best regards,

Neil

--
Neil Fernandez

```