Sources page biographical material

6.AS.2.a. TWO EQUAL SQUARES TO A SQUARE
Further subdivision of the pieces gives us 6.AS.4.
Jackson. Rational Amusement. 1821. Geometrical Puzzles, no. 13, pp. 25 & 85-86. Cut two equal squares each into two pieces to make a square.

Leske. Illustriertes Spielbuch für Mädchen. 1864? Prob. 172, p. 87. Cut one square into pieces to make two equal squares. Cuts along the diagonals.

Mittenzwey. 1880. Prob. 241, pp. 44 & 94; 1895?: 270, pp. 48 & 96; 1917: 270, pp. 44 & 92. As is Leske.
6.AS.3. THREE EQUAL SQUARES TO A SQUARE
Crambrook. 1843. P. 4, no. 21: One [Square to form] three [Squares] -- ??

"Student". Proposal [A pretty geometrical problem]. Knowledge 1 (13 Jan 1882) 229, item 184. Dissect an L-tromino into a square. Says there are 25 solutions -- editor says there are many more.

Editor. A pretty geometrical problem. Knowledge 1 (3 Mar 1882) 380. Says only the proposer has given a correct solution, which cuts off one square, then cuts the remaining double square into three parts, so the solution has four pieces. Says there are several other ways with four pieces and infinitely many with five pieces.

Hoffmann. 1893. Chap. III, no. 23: The dissected square, pp. 101 & 134 = Hoffmann Hordern, pp. 96-97, with photo. Cuts three squares identically into three pieces to form one square. Photo on p. 97 shows The Dissected Square, with box, by Jaques & Son, 1870-1895. Hordern Collection, p. 63, shows Arabian Puzzle, with box and some problem shapes to make, 1870 1890.

Loyd. Problem 3: The three squares puzzle. Tit Bits 31 (17 Oct, 7 & 14 Nov 1896) 39, 97 & 112. Quadrisect 3 x 1 rectangle to a square. Sphinx (i.e. Dudeney) notes it also can be done with three pieces.

M. Adams. Indoor Games. 1912. The divided square, p. 349 with figs. on pp. 346-347. 3 squares, 4 cuts, 7 pieces.

Loyd. Cyclopedia. 1914. Pp. 14 & 341. = SLAHP: Three in one, pp. 44 & 100. Viewed as a 3 x 1 rectangle, solution uses 2 cuts, 3 pieces. Viewed as 3 squares, there are 3 cuts, 6 pieces.

Johannes Lehmann. Kurzweil durch Mathe. Urania Verlag, Leipzig, 1980. No. 6, pp. 61 & 160. Claims the problem is posed by Abu'l-Wefa, late 10C, though other problems in this section are not strictly as posed by the historic figures cited. Two of the squares to be divided into 8 parts so all nine parts make a square. The solution has the general form of the quadrisection of the square of side 2 folded around to surround a square of side 1 (as in Perigal's(?) dissection proof of the Theorem of Pythagoras), thus forming the square of side 3. The four quadrisection pieces are cut into two triangles of sides: 1, 3/2, (1+2)/2 and 1, 3/2, (2-1)/2. Two of each shape assemble into a square of side 1 which can be viewed as having a diagonal cut and then cuts from the other corners to the diagonal, cutting off (2-1)/2 on the diagonal.