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Concept
Duncan Sommerville
Summary
Duncan MacLaren Young Sommerville (1879–1934) was a Scottish mathematician and astronomer. He compiled a bibliography on non-Euclidean geometry and also wrote a leading textbook in that field. He also wrote Introduction to the Geometry of N Dimensions, advancing the study of polytopes. He was a co-founder and the first secretary of the New Zealand Astronomical Society.
Sommerville was also an accomplished watercolourist, producing a series New Zealand landscapes.
The middle name 'MacLaren' is spelt using the old orthography M'Laren in some sources, for example the records of the Royal Society of Edinburgh.
Sommerville was born on 24 November 1879 in Beawar in India, where his father the Rev Dr James Sommerville, was employed as a missionary by the United Presbyterian Church of Scotland. His father had been responsible for establishing the hospital at Jodhpur, Rajputana.
The family returned home to Perth, Scotland, where Duncan spent 4 years at a private school, before completing his education at Perth Academy. His father died in his youth. He lived with his mother at 12 Rose Terrace. Despite his father's death, he won a scholarship, allowing him to continue his studies to university level.
He then studied mathematics at the University of St Andrews in Fife, graduating MA in 1902. He then began as an assistant lecturer at the university. In 1905 he gained his doctorate (DSc) for his thesis, Networks of the Plane in Absolute Geometry and was promoted to lecturer. He continued teaching mathematics at St Andrews until 1915.
In projective geometry the method of Cayley–Klein metrics had been used in the 19th century to model non-euclidean geometry. In 1910 Duncan wrote "Classification of geometries with projective metrics". The classification is described by Daniel Corey as follows:
He classifies them into 9 types of plane geometries, 27 in dimension 3, and more generally 3n in dimension n. A number of these geometries have found applications, for instance in physics.
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