# Lee Sallows

Lee Sallows
Born April 30, 1944
Welwyn, Hertfordshire
Residence Nijmegen, The Netherlands
Nationality English
Fields Recreational mathematics
Known for Golygons
Alphamagic squares
Geometric magic squares
Self-tiling tile sets
Self-enumerating sentences

Lee Cecil Fletcher Sallows (born April 30, 1944) is a British electronics engineer known for his contributions to recreational mathematics. He is particularly noted as the inventor of golygons, self-enumerating sentences, and geomagic squares. Sallows has an Erdős number of 2.[1][2]

## Recreational mathematics

Sallows is an expert on the theory of magic squares[3] and has invented several variations on them, including alphamagic squares[4][5] and geomagic squares.[6] The latter invention caught the attention of mathematician Peter Cameron who has said that he believes that "an even deeper structure may lie hidden beyond geomagic squares"[7]

In 1984 Lee Sallows invented the self-enumerating sentence—a sentence that inventories its own letters. Following failure in his attempt to write a computer program to generate such sentences, he constructed a so-called electronic Pangram Machine, among the results of which was the following sentence that appeared in Douglas Hofstadter's Metamagical Themas column in Scientific American in October 1984:[8]

This pangram contains four as, one b, two cs, one d, thirty es, six fs, five gs, seven hs, eleven is, one j, one k, two ls, two ms, eighteen ns, fifteen os, two ps, one q, five rs, twenty-seven ss, eighteen ts, two us, seven vs, eight ws, two xs, three ys, & one z.

A golygon is a polygon containing only right angles, such that adjacent sides exhibit consecutive integer lengths. Golygons were invented and named by Sallows[2] and introduced by A.K. Dewdney in the Computer Recreations column of the July 1990 issue of Scientific American.[9]

In 2012 Sallows invented and named self-tiling tile sets—a new generalization of rep-tiles.[10]

One of Sallows's geomagic squares

## Personal life

Lee Sallows is the only son of Florence Eliza Fletcher and Leonard Gandy Sallows. He was born on 30 April 1944 at Brocket Hall in Hertfordshire, England, and grew up in the district of Upper Clapton in northeast London. Sallows attended Dame Alice Owen's School, then located at The Angel, Islington, but failed to settle in and was without diplomas when he left at age 17. Knowledge gained via interest in short-wave radio enabled him to find work as a technician within the electronics industry. In 1970 he moved to Nijmegen in the Netherlands, where until 2009, he worked as an electronic engineer at Radboud University. In 1973 Sallows met up with his Dutch partner Evert Lamfers, now a cardiologist, with whom he has lived ever since.

## Bibliography

• 2014 Sallows, Lee "More On Self-tiling Tile Sets", Mathematics Magazine, April 2014
• 2012 Sallows, Lee. "On Self-Tiling Tile Sets", Mathematics Magazine, December, 2012
• 2012 "Geometric Magic Squares: A Challenging New Twist Using Colored Shapes Instead of Numbers", Dover Publications, ISBN 0486489094
• 1997 "The Lost Theorem", The Mathematical Intelligencer 1997 19; 4: 51–54.
• 1995 "The Impossible Problem", The Mathematical Intelligencer 1995 17; 1: 27–33.
• 1994 "Alphamagic Squares", In: The Lighter Side of Mathematics pp 305–39, Edited by R.K. Guy and R.E. Woodrow, pub. by The Mathematical Association of America, 1994, ISBN 0-88385-516-X
• 1992 Sallows, Lee (1992). "New pathways in serial isogons". The Mathematical Intelligencer 14: 55–67. doi:10.1007/BF03025216.
• 1991 Sallows, Lee; Gardner, Martin; Guy, Richard K.; Knuth, Donald (1991). "Serial isogons of 90 degrees". Mathematics Magazine 64 (5): 315–324. doi:10.2307/2690648. JSTOR 2690648.
• 1990 "A Curious New Result in Switching Theory", The Mathematical Intelligencer 1990; 12: 21–32.
• 1987 "In Quest of a Pangram", In: A Computer Science Reader, pp 200–20, Edited by EA Weiss, Springer-Verlag, New York, ISBN 0-387-96544-0
• 1986 "Co-Descriptive Strings", (Lee Sallows & Victor L Eijkhout), Mathematical Gazette 1986; 70: 1–10