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Lee Cecil Fletcher Sallows (born April 30, 1944) is a British electronics engineer known for his contributions to
recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...
. He is particularly noted as the inventor of
golygon A golygon, or more generally a serial isogon of 90°, is any polygon with all right angles (a rectilinear polygon) whose sides are consecutive integer lengths. Golygons were invented and named by Lee Sallows, and popularized by A.K. Dewdney in a ...
s, self-enumerating sentences, and geomagic squares.


Recreational mathematics

Sallows is an expert on the theory of
magic squares In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The " ...
and has invented several variations on them, including
alphamagic square An alphamagic square is a magic square that remains magic when its numbers are replaced by the number of letters occurring in the name of each number. Hence 3 would be replaced by 5, the number of letters in "three". Since different languages will ...
s and geomagic squares. The latter invention caught the attention of mathematician
Peter Cameron Peter Cameron may refer to: * Peter Cameron (entomologist) (1847–1912), English entomologist who specialised in Hymenoptera * Peter Cameron (mathematician) (born 1947), Australian mathematician, joint winner of the 2003 Euler Medal * Peter Camero ...
who has said that he believes that "an even deeper structure may lie hidden beyond geomagic squares" In "The lost theorem" published in 1997 he showed that every 3 × 3 magic square is associated with a unique parallelogram on the
complex plane In mathematics, the complex plane is the plane (geometry), plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, call ...
, a discovery that had escaped all previous researchers from ancient times down to the present day. A
golygon A golygon, or more generally a serial isogon of 90°, is any polygon with all right angles (a rectilinear polygon) whose sides are consecutive integer lengths. Golygons were invented and named by Lee Sallows, and popularized by A.K. Dewdney in a ...
is a
polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...
containing only
right angle In geometry and trigonometry, a right angle is an angle of exactly 90 Degree (angle), degrees or radians corresponding to a quarter turn (geometry), turn. If a Line (mathematics)#Ray, ray is placed so that its endpoint is on a line and the ad ...
s, such that adjacent sides exhibit consecutive
integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
lengths. Golygons were invented and named by Sallows and introduced by A.K. Dewdney in the ''Computer Recreations'' column of the July 1990 issue of
Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...
. In 2012 Sallows invented and named self-tiling tile sets—a new generalization of
rep-tiles In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape. The term was coined as a pun on animal reptiles by recreational mathematician Solomon W. Golomb and popularized by Ma ...
.


Triangle theorem

In 2014 Sallows discovered a previously unnoticed result, a way of using the
medians The Medes were an Iron Age Iranian people who spoke the Median language and who inhabited an area known as Media between western and northern Iran. Around the 11th century BC, they occupied the mountainous region of northwestern Iran and ...
to divide any triangle into three smaller triangles, all congruent with one another. Repeating the process on each triangle yields triangles similar to the original but a ninth the area.


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 Brocket Hall is a Neoclassical architecture, neo-classical English country house, country house set in a large park at the western side of the urban area of Welwyn Garden City in Hertfordshire, England. The estate is equipped with two golf cour ...
in
Hertfordshire Hertfordshire ( or ; often abbreviated Herts) is a ceremonial county in the East of England and one of the home counties. It borders Bedfordshire to the north-west, Cambridgeshire to the north-east, Essex to the east, Greater London to the ...
, England, and grew up in the district of
Upper Clapton Clapton is a district of east London, England, in the London Borough of Hackney. Clapton is divided into Upper Clapton, in the north, and Lower Clapton to the south. Clapton railway station lies north-east of Charing Cross. Geography and orig ...
in northeast London. Sallows attended
Dame Alice Owen's School Dame Alice Owen's School (DAOS, or simply Dame Alice Owen's or Owen's) is an 11–18 co-educational, partially selective secondary school and sixth form with academy status in Potters Bar, Hertfordshire, England. It is part of the Dame Al ...
, then located at
The Angel, Islington The Angel, Islington, is a historic landmark and a series of buildings that have stood on the corner of Islington High Street and Pentonville Road in Islington, London, England. The land originally belonged to the Clerkenwell Priory and has ha ...
, but failed to settle in and was without diplomas when he left at age 17. Knowledge gained via interest in
short-wave radio Shortwave radio is radio transmission using radio frequencies in the shortwave bands (SW). There is no official definition of the band range, but it always includes all of the high frequency band (HF), which extends from 3 to 30 MHz (app ...
enabled him to find work as a technician within the electronics industry. In 1970 he moved to
Nijmegen Nijmegen ( , ; Nijmeegs: ) is the largest city in the Dutch province of Gelderland and the ninth largest of the Netherlands as a whole. Located on the Waal River close to the German border, Nijmegen is one of the oldest cities in the ...
in the Netherlands, where until 2009, he worked as an electronic engineer at
Radboud University Radboud University (abbreviated as RU, , formerly ) is a public research university located in Nijmegen, Netherlands. RU has seven faculties and more than 24,000 students. Established in 1923, Radboud University has consistently been included in ...
. In 1975 Sallows met his partner Evert Lamfers, a Dutch
cardiologist Cardiology () is the study of the heart. Cardiology is a branch of medicine that deals with disorders of the heart and the cardiovascular system. The field includes medical diagnosis and treatment of congenital heart defects, coronary artery di ...
,Farewell to cardiologist Evert Lamfers
/ref> 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, * 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, * 1992 * 1991 * 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, * 1986 "Co-Descriptive Strings", (Lee Sallows & Victor L Eijkhout), Mathematical Gazette 1986; 70: 1–10


References


External links

* {{DEFAULTSORT:Sallows, Lee Cecil Fletcher Recreational mathematicians Mathematics popularizers Combinatorial game theorists Magic squares People from Nijmegen 1944 births Living people