Duncan MacLaren Young SommervilleFRSEFRAS (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.
Sommerville was born on 24 November 1879 in BeawarinIndia, 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.[2] Despite his father's death, he won a scholarship, allowing him to continue his studies to university level.[3]
He then studied mathematics at the University of St AndrewsinFife, 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.[4]
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.
In 1911 Sommerville published his compiled bibliography of works on non-euclidean geometry, and it received favorable reviews.[8][9] In 1970 Chelsea Publishing issued a second edition which referred to collected works then available of some of the cited authors.[10]
In 1915 Sommerville went to New Zealand to take up the Chair of Pure and Applied Mathematics at the Victoria College of Wellington.
Duncan became interested in honeycombs and wrote "Division of space by congruent triangles and tetrahedra" in 1923.[12] The following year he extended results to n-dimensional space.[13]
Sommerville used geometry to describe the voting theory of a preferential ballot.[14] He addressed Nanson's method where n candidates are ordered by voters into a sequence of preferences. Sommerville shows that the outcomes lie in n!simplexes that cover the surface of an n − 2 dimensional spherical space.
When his Introduction to Geometry of N Dimensions appeared in 1929, it received a positive review from B. C. Wong in the American Mathematical Monthly.[15]
