Gavin Theobald improved by one piece my 9-piece dissection of a {12/3} to a square by one piece. Furthermore, while I turned over two pieces in my dissection, his dissection doesn't turn over any pieces! The dissection still fits in the chapter based on tessellations: Gavin effectively dissects the {12/3} into five pieces, with which he can then tile the plane. If we superpose a tiling of squares of area equal to the area of the {12/3}, that forces three more pieces, for a total of eight pieces.
Here is Gavin's lovely dissection!
Originally I had a 10-piece dissection in Fig. H7 of my revision of Harry Lindgren's book. I had used the dissection of two squares to one, where the larger square is of area equal to the area of the {12/3} minus the four "outside crowns", and the smaller square is of area equal to that of the outside crowns. The area of the three pieces in Gavin's dissection (colors pink, medium blue, and dark blue) is precisely that of the four outside crowns.
Last updated February 15, 2019.