Further reading:

(All the following sources either allowed equally sized squares side by side
or did not allow equally sized squares at all.)


Erich Friedman looked at tiling a square into smaller squares.
See http://www.stetson.edu/~efriedma/mathmagic/1298.html 

Martin Gardner, The Second Scientific American Book of Mathematical
Puzzles and Diversions, Simon and Schuster, New York, 1961.
 - Discusses the problem of dissecting a square into squares of
   different sizes.  At the time, the solution with the fewest squares
   used 24 squares.  

Eric Weisstein, "Perfect Square Dissection" and "Mrs. Perkins' Quilt" in
CRC Concise Encyclopedia of Mathematics, CRC Press, 1998.
 - The published version of his old "Treasure Trove" site which is
   entangled in that lawsuit now.  


Bouwkamp, C. J. and Duijvestijn, A. J. W. ``Catalogue of Simple Perfect
Squared Squares of Orders 21 Through 25.'' Eindhoven Univ.
Technology, Dept. Math, Report 92-WSK-03, Nov. 1992.
 - Includes the 21-square, 112x112 solution to the above problem.


Various sources cited in Weisstein:

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays,
13th ed. New York: Dover, pp. 115-116, 1987.

Beiler, A. H. Recreations in the Theory of Numbers: The Queen of Mathematics
Entertains. New York: Dover, pp. 157-161, 1966.

Brooks, R. L.; Smith, C. A. B.; Stone, A. H.; and Tutte, W. T. ``The
Dissection of Rectangles into Squares.'' Duke Math. J. 7, 312-340, 1940.

Descartes, B. ``Division of a Square into Rectangles.'' Eureka, No. 34,
31-35, 1971.

Duijvestijn, A. J. W. ``A Simple Perfect Square of Lowest Order.''
J. Combin. Th. Ser. B 25, 240-243, 1978.

Duijvestijn, A. J. W. ``A Lowest Order Simple Perfect 2 x 1 Squared
Rectangle.'' J. Combin. Th. Ser. B 26, 372-374, 1979.

Duijvestijn, A. J. W. ftp://ftp.cs.utwente.nl/pub/doc/dvs/TableI.

Gardner, M. ``Squaring the Square.'' Ch. 17 in The Second Scientific
American Book of Mathematical Puzzles & Diversions: A New Selection.
New York: Simon and Schuster, pp. 186-209, 1961.

Gardner, M. Fractal Music, Hypercards, and More: Mathematical Recreations
from Scientific American Magazine. New York: W. H. Freeman, pp. 172-174, 1992.

Kraitchik, M. Mathematical Recreations. New York: W. W. Norton, 1942.

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover,
pp. 15 and 32-33, 1979.

Mauldin, R. D. (Ed.) The Scottish Book: Math at the Scottish Cafe
Boston, MA: Birkhäuser, 1982.

Moron, Z. ``O rozk\l adach prostokatów na kwadraty.'' Przeglad
matematyczno-fizyczny 3, 152-153, 1925.

Reichert, H. and Toepken, H. Jahresber. deutschen math. Verein. 50, 1940.

Skinner, J. D. II. Squared Squares: Who's Who & What's What. Published by
the author, 1993.

Sloane, N. J. A. Sequence A006983/M4482 in ``An On-Line Version of the
Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and extended
entry in Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer
Sequences. San Diego: Academic Press, 1995.

Sprague, R. ``Beispiel einer Zerlegung des Quadrats in lauter verschiedene
Quadrate.'' Math. Z. 45, 607-608, 1939.

Steinhaus, H. Mathematical Snapshots, 3rd American ed. New York: Oxford
University Press, 1983.

Weisstein, E. W. ``Perfect Squares.'' Mathematica notebook
PerfectSquare.m.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry.
London: Penguin, p. 242, 1991.

Willcocks, T. H. Fairy Chess Review 7, 1948.

Willcocks, T. H. ``A Note on Some Perfect Squared Squares.'' Canad.
J. Math. 3, 304-308, 1951.



In an archived usenet discussion on the subject, one poster writes:

The first squared rectangle [rectangle dissected into different squares]
was found in 1925 by Z. Moron (see Przeglad Mat. Fiz. 3, 152-153, 1925).

He then cites the following, one of which was already listed above:

 - Tables relating to simple squared rectangles of orders 9 to 14
   by
   C.J.Bouwkamp, A.J.W.Duijvestijn and P.Medema
   Published by Eindhoven University of Technology, EUT Report 86-WSK-03
                                                    ISSN 0167-9708
   (note: not recommended: hard to read!)
 - Catalogue of Simple Perfect Squared Squares of orders 21 through 25
   by
   C.J.Bouwkamp and A.J.W.Duijvestijn
   EUT Report 92-WSK-03, Eindhoven, November 1992
 - Album of Simple Perfect Squared Squares of order 26
   by
   C.J.Bouwkamp and A.J.W.Duijvestijn
   EUT Report 94-WSK-02, Eindhoven, December 1994

He adds: download from; ftp.cs.utwente.nl/pub/doc/dvs/  



Perhaps of more interest is the "Mrs. Perkins' Quilt" problem which
includes dissections which include squares of the same size.


Conway, J. H. ``Mrs. Perkins's Quilt.'' Proc. Cambridge Phil. Soc. 60,
363-368, 1964.

Dudeney, H. E. Problem 173 in Amusements in Mathematics. New York: Dover,
1917.

Dudeney, H. E. Problem 177 in 536 Puzzles & Curious Problems. New York:
Scribner, 1967.

Gardner, M. ``Mrs. Perkins' Quilt and Other Square-Packing Problems.'' Ch. 11
in Mathematical Carnival: A New Round-Up of Tantalizers and
Puzzles from Scientific American. New York: Vintage, 1977.

Sloane, N. J. A. Sequence A005670/M3267 in ``An On-Line Version of the
Encyclopedia of Integer Sequences''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J.
A. and Plouffe, S. The Encyclopedia of Integer Sequences. San
Diego: Academic Press, 1995.

Trustrum, G. B. ``Mrs. Perkins's Quilt.'' Proc. Cambridge Phil. Soc. 61, 7-11,
1965.