

A362939


a(n) = minimum number of pieces needed to dissect a regular nsided polygon into a rectangle (conjectured).


3



2, 1, 4, 3, 5, 4, 7, 4, 9, 5, 10, 7, 10, 9
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OFFSET

3,1


COMMENTS

The dimensions of the rectangle can be anything you want, as long as it is a rectangle.
Turning over is allowed. The pieces must be bounded by simple curves to avoid difficulties with nonmeasurable sets.
Apart from changing "square" to "rectangle", the rules are the same as in A110312.
I do not know which of these values have been proved to be minimal. Probably only a(3)=2 and a(4)=1.
The three related sequences A110312, A362938, A362939 are exceptions to the usual OEIS policy of requiring that all terms in sequences must be known exactly. These sequences are included because of their importance and in the hope that someone will establish the truth of some of the conjectured values.


LINKS

N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)


EXAMPLE

See our paper "On dissecting polygons into rectangles" for illustrations of a(n) for all n <= 16 except n=13 and n=15.


CROSSREFS



KEYWORD

nonn,more,hard


AUTHOR



STATUS

approved



