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
An orthography is a set of conventions for writing a language, including norms of spelling, hyphenation, capitalization, word breaks, emphasis, and punctuation.
Most transnational languages in the modern period have a writing system, and mos ...
M'Laren in some sources, for example the records of the
Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...
.
Early life
Sommerville was born on 24 November 1879 in
Beawar in
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
, 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
Jodhpur (; ) is the second-largest city in the Indian state of Rajasthan and officially the second metropolitan city of the state. It was formerly the seat of the princely state of Jodhpur State. Jodhpur was historically the capital of the Ki ...
,
Rajputana
Rājputana, meaning "Land of the Rajputs", was a region in the Indian subcontinent that included mainly the present-day Indian state of Rajasthan, as well as parts of Madhya Pradesh and Gujarat, and some adjoining areas of Sindh in modern-day ...
.
The family returned home to
Perth, Scotland
Perth (Scottish English, locally: ; gd, Peairt ) is a city in central Scotland, on the banks of the River Tay. It is the administrative centre of Perth and Kinross council area and the historic county town of Perthshire. It had a population o ...
, where Duncan spent 4 years at a private school, before completing his education at
Perth Academy
Perth Academy is a state comprehensive secondary school in Perth, Scotland. It was founded in 1696. The institution is a non-denominational one. The school occupies ground on the side of a hill in the Viewlands area of Perth, and is within the Pe ...
. 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
(Aien aristeuein)
, motto_lang = grc
, mottoeng = Ever to ExcelorEver to be the Best
, established =
, type = Public research university
Ancient university
, endowment ...
in
Fife
Fife (, ; gd, Fìobha, ; sco, Fife) is a council area, historic county, registration county and lieutenancy area of Scotland. It is situated between the Firth of Tay and the Firth of Forth, with inland boundaries with Perth and Kinross (i ...
, graduating MA in 1902. He then began as an assistant lecturer at the university. In 1905 he gained his doctorate (
DSc DSC may refer to:
Academia
* Doctor of Science (D.Sc.)
* District Selection Committee, an entrance exam in India
* Doctor of Surgical Chiropody, superseded in the 1960s by Doctor of Podiatric Medicine
Educational institutions
* Dalton State Col ...
) 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 metric
In mathematics, a Cayley–Klein metric is a metric on the complement of a fixed quadric in a projective space which is defined using a cross-ratio. The construction originated with Arthur Cayley's essay "On the theory of distance"Cayley (1859), p ...
s 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 3
n in dimension n. A number of these geometries have found applications, for instance in physics.
In 1910 Sommerville reported to the
British Association on the need for a
bibliography
Bibliography (from and ), as a discipline, is traditionally the academic study of books as physical, cultural objects; in this sense, it is also known as bibliology (from ). English author and bibliographer John Carter describes ''bibliography ...
on
non-euclidean geometry, noting that the field had no International Association like the
Quaternion Society to sponsor it.
In 1911 Sommerville published his compiled bibliography of works on non-euclidean geometry, and it received favorable reviews. In 1970
Chelsea Publishing issued a second edition which referred to
collected works then available of some of the cited authors.
Sommerville was elected a Fellow of the
Royal Society of Edinburgh
The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...
in 1911. His proposers were
Peter Redford Scott Lang
Sir Peter Redford Scott Lang VD FRSE (1850–1926) was a Scottish mathematician and Regius Professor at the University of St Andrews. In the 1880s he instituted “Common Dinners” to bring the students together for joint meals (often referred ...
,
Robert Alexander Robertson,
William Peddie and
George Chrystal.
Family
In 1912 he married Louisa Agnes Beveridge.
Work in New Zealand
In 1915 Sommerville went to
New Zealand
New Zealand ( mi, Aotearoa ) is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and over 700 smaller islands. It is the sixth-largest island count ...
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. The following year he extended results to ''n''-dimensional space.
He also discovered the
Dehn–Sommerville equations In mathematics, the Dehn–Sommerville equations are a complete set of linear relations between the numbers of faces of different dimension of a simplicial polytope. For polytopes of dimension 4 and 5, they were found by Max Dehn in 1905. Their gen ...
for the number of faces of
convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Most texts. use the term "polytope" for a bounded convex polytope, and the wo ...
s.
Sommerville used geometry to describe the
voting theory of a
preferential ballot. 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'' !
simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. ...
es 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
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America.
The ''American Mathematical Monthly'' is an e ...
.
[B.C. Wong (1931) "Recent publications", ]American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America.
The ''American Mathematical Monthly'' is an e ...
38(5):286–7
Sommerville was co-founder and first secretary of the
New Zealand Astronomical Society (1920). He was President of Section A of the
Australasian Association for the Advancement of Science meeting, Adelaide (1924). In 1926 he became a fellow of the
Royal Astronomical Society
(Whatever shines should be observed)
, predecessor =
, successor =
, formation =
, founder =
, extinction =
, merger =
, merged =
, type = NGO ...
.
He died in New Zealand on 31 January 1934.
Textbooks
* 1914: ''The Elements of Non-Euclidean Geometry'', William P. Milne editor, Bell's Mathematical Series for Schools and Colleges,
G. Bell & Sons.
The Elements of Non-Euclidean Geometry link from
University of Michigan
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
Historical Math Collection.
* 1930: ''An Introduction to the Geometry of N Dimensions'', New York,
E. P. Dutton
E. P. Dutton was an American Publishing, book publishing company. It was founded as a book retailer in Boston, Massachusetts, in 1852 by Edward Payson Dutton. Since 1986, it has been an imprint of Penguin Group.
Creator
Edward Payson Dutton ( ...
, (Dover Publications edition, 1958)
* 1933
Analytical Conicsfrom
Google Books
Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical c ...
* 1934: ''Analytical Geometry of Three Dimensions.''
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press
A university press is an academic publishing hou ...
.
References
Citations
Sources
* H.W. Turnbull (1934) "Duncan M. Y. Sommerville",
Journal of the London Mathematical Society 9(4):316–18.
* B. A. Rosenfeld (1979) "The Works on Geometry of Duncan Sommerville", ''Istoriko-Matematicheskie Issledovania'', .
External links
*
Obituary Monthly Notices of the Royal Astronomical Society
''Monthly Notices of the Royal Astronomical Society'' (MNRAS) is a peer-reviewed scientific journal covering research in astronomy and astrophysics. It has been in continuous existence since 1827 and publishes letters and papers reporting orig ...
Vol. 95, pp. 330–331.
*C.J. Seelye (1974
Mathematics At Victoria In Retrospect Notes for a talk to the Mathematics and Physics Society, from
NZETC.
{{DEFAULTSORT:Sommerville, Duncan M. Y.
1879 births
1934 deaths
People from Perth, Scotland
People from Wellington City
People educated at Perth Academy
Alumni of the University of St Andrews
Fellows of the Royal Society of Edinburgh
Geometers
20th-century New Zealand astronomers
20th-century New Zealand historians
20th-century Scottish historians
20th-century New Zealand mathematicians
20th-century Scottish mathematicians
20th-century New Zealand painters
20th-century New Zealand male artists
Scottish watercolourists
Victoria University of Wellington faculty
Scottish emigrants to New Zealand
British historians of mathematics
Fellows of the Royal Astronomical Society
Academics of the University of St Andrews
20th-century Scottish painters
Scottish male painters
20th-century Scottish male artists