Stuart Anderson of http://www.squaring.net/ sent me an interesting letter. The material he's put on his site is well worth a look. --Ed Pegg Jr Ed, I have recently added a new line of tilings to my website. Simple Perfect Right-Angled Isosceles Triangled Squares or SPRAITS's as the abbreviation is known. The theory of SPRAITS's is related to that of Squared Rectangles and Squared Squares and was the subject of a paper recently published by two of the original authors of the 1940 'The dissection of rectangles into squares' paper, in collaboration with JD Skinner. Skinner's discovery in the 1990's of a perfect RAIT square dissection inspired the research paper ; J.D. Skinner II, C.A.B. Smith, and W.T. Tutte, On the Dissection of Rectangles into Right-Angled Isosceles Triangles, Journal of Combinatorial Theory Series B 80 (2000), 277-319. Unfortunately CAB Smith and Bill Tutte have both passed away since that paper was published in 2000. However Skinner and Geoffrey H. Morley have been working on SPRAIT dissections for over a decade and have compiled a large catalog of SPRAITS's tilings. Geoffrey H. Morley has discovered the largest number of SPRAIT tilings. He has made his catalog available to me. It contains over 14600 SPRAITS's. I have created javascript code to display all known SPRAITS's on my website and they can be selected and displayed in manner similar to the Squared Squares and Rectangles on my site at www.squaring.net. cheers, Stuart Anderson