OFFSET

1,3

COMMENTS

"Distinct" here means that dissections differing only by a rotation and/or reflection are not counted as different (see A189243).

The first time the pieces can be made to all have different shapes (but the same area) is at n=7 - see Descartes (1971) and the illustration; also Wells, Weisstein. - N. J. A. Sloane, Dec 05 2012

REFERENCES

David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, pp. 15-16.

LINKS

Blanche Descartes, Divisions of a square into rectangles, Eureka, No. 34 (1971), 31-35.

R. Häggkvist, P.-O. Lindberg, and B. Lindström, Dissecting a square into rectangles of equal area, Discr. Math. 47 (1983), 321-323.

Johan Nilsson, Illustrations for terms up to a(6)..

N. J. A. Sloane, Blanche Descartes's dissection into 7 pieces with equal areas but different shapes.

Eric Weisstein, Blanche's Dissection.

EXAMPLE

There are six ways to dissect a square into four rectangles of equal area, so a(4)=6:

+-+-----+ +-+-+---+ +-+-----+ +-+-+-+-+ +-+---+-+ +---+---+

| | | | | | | | | | | | | | | | | | | | | |

| | | | | | | | | | | | | | | | | | | | | |

| +--+--+ | | | | | +-----+ | | | | | | | | | | | |

| | | | | | +---+ | | | | | | | | | +---+ | +---+---+

| | | | | | | | | |_____| | | | | | | | | | | | |

| | | | | | | | | | | | | | | | | | | | | | |

| | | | | | | | | | | | | | | | | | | | | | |

+-+--+--+ +-+-+---+ +-+-----+ +-+-+-+-+ +-+---+-+ +---+---+

CROSSREFS

KEYWORD

hard,more,nonn,nice

AUTHOR

Hans Riesebos (hans.riesebos(AT)wanadoo.nl) and Herman Beeksma, Jun 03 2005

STATUS

approved