Duncan Sommerville

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Duncan Sommerville_table_infobox_0

Duncan M. Y. SommervilleDuncan Sommerville_header_cell_0_0_0
BornDuncan Sommerville_header_cell_0_1_0 24 November 1879

Beawar, Rajputana, IndiaDuncan Sommerville_cell_0_1_1

DiedDuncan Sommerville_header_cell_0_2_0 31 January 1934

Wellington, New ZealandDuncan Sommerville_cell_0_2_1

NationalityDuncan Sommerville_header_cell_0_3_0 ScottishDuncan Sommerville_cell_0_3_1
CitizenshipDuncan Sommerville_header_cell_0_4_0 United KingdomDuncan Sommerville_cell_0_4_1
Alma materDuncan Sommerville_header_cell_0_5_0 St Andrews UniversityDuncan Sommerville_cell_0_5_1
Known forDuncan Sommerville_header_cell_0_6_0 Textbooks on geometryDuncan Sommerville_cell_0_6_1
FieldsDuncan Sommerville_header_cell_0_7_0 MathematicsDuncan Sommerville_cell_0_7_1
InstitutionsDuncan Sommerville_header_cell_0_8_0 St Andrews University (1904–13)

Wellington University (1913–34)Duncan Sommerville_cell_0_8_1

Prof Duncan MacLaren Young Sommerville FRSE FRAS (1879–1934) was a Scottish mathematician and astronomer. Duncan Sommerville_sentence_0

He compiled a bibliography on non-Euclidean geometry and also wrote a leading textbook in that field. Duncan Sommerville_sentence_1

He also wrote Introduction to the Geometry of N Dimensions, advancing the study of polytopes. Duncan Sommerville_sentence_2

He was a co-founder and the first secretary of the New Zealand Astronomical Society. Duncan Sommerville_sentence_3

Sommerville was also an accomplished watercolourist, producing a series New Zealand landscapes. Duncan Sommerville_sentence_4

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. Duncan Sommerville_sentence_5

Early life Duncan Sommerville_section_0

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. Duncan Sommerville_sentence_6

His father had been responsible for establishing the hospital at Jodhpur, Rajputana. Duncan Sommerville_sentence_7

The family returned home to Perth, Scotland, where Duncan spent 4 years at a private school, before completing his education at Perth Academy. Duncan Sommerville_sentence_8

His father died in his youth. Duncan Sommerville_sentence_9

He lived with his mother at 12 Rose Terrace. Duncan Sommerville_sentence_10

Despite his father's death, he won a scholarship, allowing him to continue his studies to university level. Duncan Sommerville_sentence_11

He then studied Mathematics at the University of St Andrews in Fife, graduating MA in 1902. Duncan Sommerville_sentence_12

He then began as an Assistant Lecturer at the university. Duncan Sommerville_sentence_13

In 1905 he gained his doctorate (DSc) for his thesis, Networks of the Plane in Absolute Geometry and was promoted to Lecturer. Duncan Sommerville_sentence_14

He continued teaching Mathematics at St Andrews until 1915. Duncan Sommerville_sentence_15

In projective geometry the method of Cayley–Klein metrics had been used in the 19th century to model non-euclidean geometry. Duncan Sommerville_sentence_16

In 1910 Duncan wrote "Classification of geometries with projective metrics". Duncan Sommerville_sentence_17

The classification is described by Daniel Corey as follows: Duncan Sommerville_sentence_18

Duncan Sommerville_description_list_0

  • He classifies them into 9 types of plane geometries, 27 in dimension 3, and more generally 3 in dimension n. A number of these geometries have found applications, for instance in physics.Duncan Sommerville_item_0_0

In 1910 Sommerville reported to the British Association on the need for a bibliography on non-euclidean geometry, noting that the field had no International Association like the Quaternion Society to sponsor it. Duncan Sommerville_sentence_19

In 1911 Sommerville published his compiled bibliography of works on non-euclidean geometry, and it received favorable reviews. Duncan Sommerville_sentence_20

In 1970 Chelsea Publishing issued a second edition which referred to collected works then available of some of the cited authors. Duncan Sommerville_sentence_21

Sommerville was elected a Fellow of the Royal Society of Edinburgh in 1911. Duncan Sommerville_sentence_22

His proposers were Peter Redford Scott Lang, Robert Alexander Robertson, William Peddie and George Chrystal. Duncan Sommerville_sentence_23

Family Duncan Sommerville_section_1

In 1912 he married Louisa Agnes Beveridge. Duncan Sommerville_sentence_24

Work in New Zealand Duncan Sommerville_section_2

In 1915 Sommerville went to New Zealand to take up the Chair of Pure and Applied Mathematics at the Victoria College of Wellington. Duncan Sommerville_sentence_25

Duncan became interested in honeycombs and wrote "Division of space by congruent triangles and tetrahedra" in 1923. Duncan Sommerville_sentence_26

The following year he extended results to n-dimensional space. Duncan Sommerville_sentence_27

He also discovered the Dehn–Sommerville equations for the number of faces of convex polytopes. Duncan Sommerville_sentence_28

Sommerville used geometry to describe the voting theory of a preferential ballot. Duncan Sommerville_sentence_29

He addressed Nanson's method where n candidates are ordered by voters into a sequence of preferences. Duncan Sommerville_sentence_30

Sommerville shows that the outcomes lie in n ! Duncan Sommerville_sentence_31

simplexes that cover the surface of an n − 2 dimensional spherical space. Duncan Sommerville_sentence_32

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. Duncan Sommerville_sentence_33

Sommerville was co-founder and first secretary of the New Zealand Astronomical Society (1920). Duncan Sommerville_sentence_34

He was President of Section A of the Australasian Association for the Advancement of Science meeting, Adelaide (1924). Duncan Sommerville_sentence_35

In 1926 he became a fellow of the Royal Astronomical Society. Duncan Sommerville_sentence_36

He died in New Zealand on 31 January 1934. Duncan Sommerville_sentence_37

Textbooks Duncan Sommerville_section_3

Duncan Sommerville_unordered_list_1

  • 1914: The Elements of Non-Euclidean Geometry, William P. Milne editor, Bell's Mathematical Series for Schools and Colleges, G. Bell & Sons.Duncan Sommerville_item_1_1
  • , link from University of Michigan Historical Math Collection.Duncan Sommerville_item_1_2
  • 1930: An Introduction to the Geometry of N Dimensions, New York, E. P. Dutton, (Dover Publications edition, 1958)Duncan Sommerville_item_1_3
  • 1933: from Google BooksDuncan Sommerville_item_1_4
  • 1934: Analytical Geometry of Three Dimensions. Cambridge University Press.Duncan Sommerville_item_1_5

Credits to the contents of this page go to the authors of the corresponding Wikipedia page: en.wikipedia.org/wiki/Duncan Sommerville.