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We add a bit to this post: Cutting off odd numbers of equal area triangles from a unit square

Question: Given an odd integer n, how does one cover the unit square completely with n equal area triangles such that the area of each covering triangle is minimized?

One can define g(n) as the excess of the total area of the n optimal covering triangles over 1 for a particular n and try to find out the behavior of g(n) as n increases.

Note: Covering with n equal area triangles seems more complicated than cutting n equal area triangles because of the possibility of the covering triangles to overlap among themselves and also to project out beyond the square. If it can be shown that for any n, the optimal cover will feature only one of these two possibilities, that could be interesting.

Some further thoughts on this are recorded at https://nandacumar.blogspot.com/2023/05/cutting-and-covering-cluster-of.html

Nandakumar R
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  • Wasn't the case of "odd number = 1" solved here at MO? – Wlod AA May 07 '23 at 05:21
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    I am not aware of work on optimally covering the unit square with smallest equal area triangles although lots seem to have been done on (say) covering the square with identical equilateral triangles as in https://erich-friedman.github.io/packing/tricosqu/ – Nandakumar R May 07 '23 at 07:11

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