John Frankland Rigby (22 April 1933 – 29 December 2014) was an English mathematician and academic of the

University College of South Wales, Cardiff , latin_name = , image_name = Shield of the University of Cardiff.svg , image_size = 150px , caption = Coat of arms of Cardiff University , motto = cy, Gwirionedd, Undod a Chytgord , mottoeng = Truth, Unity and Concord , established = 1 ...

, when it was part of the

University of Wales The University of Wales (Welsh language, Welsh: ''Prifysgol Cymru'') is a confederal university based in Cardiff, Wales. Founded by royal charter in 1893 as a federal university with three constituent colleges – Aberystwyth, Bangor and Cardiff � ...

, and of its successor

Cardiff University , latin_name = , image_name = Shield of the University of Cardiff.svg , image_size = 150px , caption = Coat of arms of Cardiff University , motto = cy, Gwirionedd, Undod a Chytgord , mottoeng = Truth, Unity and Concord , established = 1 ...

. Working in the field of

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, he became an authority on the relationship between maths and ornamental art and was national Secretary of the

Mathematical Association The Mathematical Association is a professional society concerned with mathematics education in the UK. History It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in ...

from 1989 to 1996.

Early life

A native of

Bolton Bolton (, locally ) is a large town in Greater Manchester in North West England, formerly a part of Lancashire. A former mill town, Bolton has been a production centre for textiles since Flemish weavers settled in the area in the 14th ce ...

, Lancashire, now part of

Greater Manchester Greater Manchester is a metropolitan county and combined authority area in North West England, with a population of 2.8 million; comprising ten metropolitan boroughs: Manchester, Salford, Bolton, Bury, Oldham, Rochdale, Stockport, Tamesid ...

, Rigby was the son of Fred Frankland Rigby and Bessie M. Hodkinson, who had been married at Bolton in 1931. He was educated at

Manchester Grammar School The Manchester Grammar School (MGS) in Manchester, England, is the largest independent day school for boys in the United Kingdom. Founded in 1515 as a free grammar school next to Manchester Parish Church, it moved in 1931 to its present site at ...

and

Trinity College, Cambridge Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge or Oxford. ...

, where after graduating BA in the

Mathematical Tripos The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. It is the oldest Tripos examined at the University. Origin In its classical nineteenth-century form, the tripos was a ...

he remained for doctoral studies. His PhD dissertation, supervised by

Philip Hall Philip Hall FRS (11 April 1904 – 30 December 1982), was an English mathematician. His major work was on group theory, notably on finite groups and solvable groups. Biography He was educated first at Christ's Hospital, where he won the Thomp ...

and completed in 1958, was ''Theory of Finite Linear Groups'', and while finishing his work on this he took a job at the

Government Communications Headquarters Government Communications Headquarters, commonly known as GCHQ, is an intelligence and security organisation responsible for providing signals intelligence (SIGINT) and information assurance (IA) to the government and armed forces of the ...

(GCHQ).Gerry Leversha
Dr John Frankland Rigby
(obituary) in ''

The Mathematical Gazette ''The Mathematical Gazette'' is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive ...

'' 99 (2015), 174–175. Retrieved 2 May 2019

Career

In 1959 Rigby was appointed to his first academic job, as a lecturer in the School of Mathematics of the University College of South Wales at Cardiff, and remained there until he retired in 1996, and beyond, as he continued to work part-time for some years. During his career, he contributed many papers on

Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the ''Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms ...

. He was also a leading authority on the interface between mathematics and ornamental art, especially

Celtic art Celtic art is associated with the peoples known as Celts; those who spoke the Celtic languages in Europe from pre-history through to the modern period, as well as the art of ancient peoples whose language is uncertain, but have cultural and styli ...

and

Islamic geometric patterns Islamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures. The geo ...

, and took a close interest in traditional Japanese geometry. He visited universities in several overseas countries, especially in

Turkey Turkey ( tr, Türkiye ), officially the Republic of Türkiye ( tr, Türkiye Cumhuriyeti, links=no ), is a list of transcontinental countries, transcontinental country located mainly on the Anatolia, Anatolian Peninsula in Western Asia, with ...

, Japan, and the

Philippines The Philippines (; fil, Pilipinas, links=no), officially the Republic of the Philippines ( fil, Republika ng Pilipinas, links=no), * bik, Republika kan Filipinas * ceb, Republika sa Pilipinas * cbk, República de Filipinas * hil, Republ ...

, and also in Singapore and Canada. Rigby lectured on

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebra ...

, drawing complicated curves and perfect circles on the blackboard, where he could make "magnificently accurate diagrams". He was an active member of the

. In the 1970s he became President of its Cardiff Branch and then was national Secretary from 1989 to 1996, at conferences giving presentations of his work. He regularly provided solutions to problems raised in the ''

Mathematical Gazette ''The Mathematical Gazette'' is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive ...

'', and an obituary described his research papers as "distinguished by their precision, concise style, and freedom from jargon". With

Branko Grünbaum Branko Grünbaum ( he, ברנקו גרונבאום; 2 October 1929 – 14 September 2018) was a Croatian-born mathematician of Jewish descentGrünbaum–Rigby configuration, and

Ross Honsberger Ross Honsberger (1929–2016) was a Canadian mathematician and author on recreational mathematics. Life Honsberger studied mathematics at the University of Toronto, with a bachelor's degree, and then worked for ten years as a teacher in Toron ...

named a point in a theorem by Rigby "the Rigby point". Adrian Oldknow named inner and outer Rigby points in connection with Soddy triangles, with the Rigby points lying on the Soddy line. In retirement, Rigby began to suffer from

Parkinson's disease Parkinson's disease (PD), or simply Parkinson's, is a long-term degenerative disorder of the central nervous system that mainly affects the motor system. The symptoms usually emerge slowly, and as the disease worsens, non-motor symptoms becom ...

, but was still wanted for international conferences. With his friend

James Wiegold James "Jim" Wiegold (15 April 1934 – 4 August 2009) was a Wales, Welsh mathematician. Born in Trecenydd, Caerphilly, he earned a Doctor of Philosophy, Ph.D. at the University of Manchester, England in 1958, studying under Bernhard Neumann ...

, he took charge of Cardiff University's Mathematics Club for

sixth form In the education systems of England, Northern Ireland, Wales, Jamaica, Trinidad and Tobago and some other Commonwealth countries, sixth form represents the final two years of secondary education, ages 16 to 18. Pupils typically prepare for A-l ...

ers, drawing in students from

Cardiff High School ) , established = 1895 (Creation of earliest of predecessor schools) , closed = , type = Public (magnet) secondary , religious_affiliation = , president = , head_label = Headmaster , head = Stephen Jones , r ...

, the Cathedral School, Llandaff, Howell's School, and schools in

Monmouth Monmouth ( , ; cy, Trefynwy meaning "town on the Monnow") is a town and community in Wales. It is situated where the River Monnow joins the River Wye, from the Wales–England border. Monmouth is northeast of Cardiff, and west of London. ...

. Those attending meetings might offer solutions to problems which could not be faulted, but Rigby "would produce far more elegant ones, drawing gasps of admiration from the audience".

Private life

Rigby sang in the

Llandaff Cathedral Llandaff Cathedral ( cy, Eglwys Gadeiriol Llandaf) is an Anglican cathedral and parish church in Llandaff, Cardiff, Wales. It is the seat of the Bishop of Llandaff, head of the Church in Wales Diocese of Llandaff. It is dedicated to Saint Pe ...

choir and also wrote music for it. From his mathematical interest in art, he went on to create his own patterns and designs, which he turned into Christmas cards, and some were embroidered for cathedral

hassocks Hassocks is a large village and civil parish in the Mid Sussex District of West Sussex, England. Its name is believed to derive from the tufts of grass found in the surrounding fields. Located approximately north of Brighton, with a populat ...

. He belonged to a Folk Dance Society and enjoyed

rambling Walking is one of the most popular outdoor recreational activities in the United Kingdom, and within England and Wales there is a comprehensive network of rights of way that permits access to the countryside. Furthermore, access to much unculti ...

in the Lake District and elsewhere. Rigby died on 29 December 2014 at the

University Hospital of Wales University Hospital of Wales ( cy, Ysbyty Athrofaol Cymru) (UHW), also known as the Heath Hospital, is a major 1,000-bed hospital in the Heath district of Cardiff, Wales. UHW is a teaching hospital of Cardiff University School of Medicine. Constr ...

, Cardiff, aged 81. Barry Morgan,

Archbishop of Wales The post of Archbishop of Wales was created in 1920 when the Church in Wales was separated from the Church of England and disestablished. The four historic Welsh dioceses had previously formed part of the Province of Canterbury, and so came unde ...

, and the Dean of Cardiff were the ministers for his funeral service at Llandaff Cathedral on 13 January 2015. His last address was 5, Cathedral Court, Cathedral Green, Llandaff, Cardiff.John Frankland RIGBY
at companieshouse.gov.uk. Retrieved 2 May 2019

Selected publications

*J. F. Rigby, "A Concentrated Dose of Old-Fashioned Geometry" in ''

'' 57, 402 (December 1973) 296–298 *J. F. Rigby, "On the Money–Coutts Configuration of Nine Anti-Tangent Cycles" in

Proceedings of the London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical ...

, 43 (Series 3), 1 (July 1981) 110–132
here
*J. F. Rigby, "The geometry of cycles, and generalized Laguerre inversion" in C. Davis, B. Grünbaum, F. A. Sherk, ''The Coxeter Festschrift'' (Berlin: Springer, 1981), 355—378 *J. F. Rigby, "The three circle theorem" in ''

Mathematics Magazine ''Mathematics Magazine'' is a refereed bimonthly publication of the Mathematical Association of America. Its intended audience is teachers of collegiate mathematics, especially at the junior/senior level, and their students. It is explicitly a ...

'' 55 (1982), 312 *John Rigby, "Napoleon revisited," in ''Journal of Geometry'' 33 (1988), 126–146 *

Branko Grünbaum Branko Grünbaum ( he, ברנקו גרונבאום; 2 October 1929 – 14 September 2018) was a Croatian-born mathematician of Jewish descent4)" in ''

Journal of the London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematica ...

'' 41 (Series 2) (1990), 336–346
here
*John F. Rigby, "Tritangent centres, Pascal's theorem and Thebault's problem" in ''Journal of Geometry'' (November 1995) 54:13
here
*John F. Rigby, "Brief notes on some forgotten geometrical theorems" in ''Mathematics and Informatics Quarterly'' 7 (1997) 156–158 *J. F. Rigby, "Precise Colourings of Regular Triangular Tilings" in ''The Mathematical Intelligencer'' (1998) 20:
here

Notes

External links

J. F. Rigby's research while affiliated with Hacettepe University and other places
at researchgate.net *J. F. Rigby
A Turkish interlacing pattern and the golden ratio
at

web site
Rigby points
at wolfram.com {{DEFAULTSORT:Rigby, John 1933 births 2014 deaths Academics of Cardiff University Academics of the University of Wales Alumni of Trinity College, Cambridge English mathematicians GCHQ people People educated at Manchester Grammar School People with Parkinson's disease