Sources page biographical material

6.AW.2. REP TILES
Here one is cutting a shape into congruent pieces similar to the original shape. Section 5.J is a version with similar but non congruent pieces.
Charades, Enigmas, and Riddles. 1862: prob. 34, pp. 137 & 143; 1865: prob. 578, pp. 109 & 156. Divide isosceles right triangle and a hatchet-shaped 10-omino into four congruent pieces. In the first case, they are congruent to the original, but in the second case, the pieces are right trapeziums of height 1 and bases 2 and 2½.

Dudeney. The puzzle realm. Cassell's Magazine ?? (May 1908) 713-716. No. 3: An easy dissection puzzle. Quadrisect a right trapezium in form of square plus half a square. = AM, 1917, prob. 146, pp. 35 & 170.

C. Dudley Langford. Note 1464: Uses of a geometric puzzle. MG 24 (No. 260) (Jul 1940) 209 211. Quadrisects: L tromino, P pentomino, right trapezium (trapezoid), L tetromino, isosceles trapezium, another right trapezium, two squares joined at a corner. Gives some 9 sections and asks several questions, including asking about 3 D versions.

R. Sibson. Note 1485: Comments on Note 1464. MG 24 (No. 262) (Dec 1940) 343. Says some of Langford's 4 sections also give 9 sections. Mentions some 3 D versions and 144 sections.

Howard D. Grossman. Fun with lattice points. 13. A geometric puzzle. SM 14 (1948) 157 159. Cites Langford & Sibson. Gives two 9-sections obtained from Langford's 4 sections as asserted by Sibson. Gives alternative 4- & 9-sections. Gives a method of generating infinitely many examples on both square and triangular lattices.

Gardner. SA (May 1963) = Unexpected, chap. 19. Says Golomb started considering rep tiles in 1962 and wrote three private reports on them (??NYS). Gardner describes the ideas in them.

Solomon W. Golomb. Replicating figures on the plane. MG 48 (No. 366) (Dec 1964) 403 412. Cites Langford and adds numerous examples. Defines rep k and shows all k can occur.

Roy O. Davis. Note 3151: Replicating boots. MG 50 (No. 372) (May 1966) 175.

Rochell Wilson Meyer. Mutession: a new tiling relationship among planar polygons. MTg 56 (1971) 24 27. A and B mutually tessellate if each tiles an enlargement of the other.