John Casey (mathematician)
Encyclopedia
John Casey was a respected Irish
geometer
. He is most famous for Casey's theorem
on a circle that is tangent to four other circles, an extension of the problem of Apollonius
. However, he contributed several novel proofs and perspectives on Euclidean geometry
. He and Émile Lemoine
are considered to be the co-founders of the modern geometry of the circle and the triangle.
. He subsequently entered Trinity College
as a student in 1858, and was awarded the degree of BA in 1862. He was then Mathematics Master at Kingston School (1862-1873), Professor of Higher Mathematics and Mathematical Physics at the newly founded Catholic University of Ireland
(1873-1881) and Lecturer in Mathematics at University College, Dublin (1881-1891).
and in 1880 became a member of its council. In 1881 the Academy conferred upon him the much coveted Cunningham Gold Medal. His work was also acknowledged by the Norwegian Government, among others. He was elected a member of the Societe Mathematique de France in 1884 and received the honorary degree of Doctor of Laws from the Royal University of Ireland
in 1885.
Irish people
The Irish people are an ethnic group who originate in Ireland, an island in northwestern Europe. Ireland has been populated for around 9,000 years , with the Irish people's earliest ancestors recorded having legends of being descended from groups such as the Nemedians, Fomorians, Fir Bolg, Tuatha...
geometer
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. He is most famous for Casey's theorem
Casey's theorem
In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey.- Formulation of the theorem:...
on a circle that is tangent to four other circles, an extension of the problem of Apollonius
Problem of Apollonius
In Euclidean plane geometry, Apollonius' problem is to construct circles that are tangent to three given circles in a plane . Apollonius of Perga posed and solved this famous problem in his work ; this work has been lost, but a 4th-century report of his results by Pappus of Alexandria has survived...
. However, he contributed several novel proofs and perspectives on Euclidean geometry
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
. He and Émile Lemoine
Émile Lemoine
Émile Michel Hyacinthe Lemoine was a French civil engineer and a mathematician, a geometer in particular. He was educated at a variety of institutions, including the Prytanée National Militaire and, most notably, the École Polytechnique...
are considered to be the co-founders of the modern geometry of the circle and the triangle.
Biography
He was born in Kilkenny, Ireland and educated locally at Mitchelstown, before becoming a teacher under the Board of National Education. He later became headmaster of the Central Model Schools in Kilkenny CityKilkenny
Kilkenny is a city and is the county town of the eponymous County Kilkenny in Ireland. It is situated on both banks of the River Nore in the province of Leinster, in the south-east of Ireland...
. He subsequently entered Trinity College
Trinity College, Dublin
Trinity College, Dublin , formally known as the College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin, was founded in 1592 by letters patent from Queen Elizabeth I as the "mother of a university", Extracts from Letters Patent of Elizabeth I, 1592: "...we...found and...
as a student in 1858, and was awarded the degree of BA in 1862. He was then Mathematics Master at Kingston School (1862-1873), Professor of Higher Mathematics and Mathematical Physics at the newly founded Catholic University of Ireland
Catholic University of Ireland
The Catholic University of Ireland was a Catholic university in Dublin, Ireland and was founded in 1851 following the Synod of Thurles in 1850, and in response to the Queen's University of Ireland and its associated colleges which were nondenominational...
(1873-1881) and Lecturer in Mathematics at University College, Dublin (1881-1891).
Honours and Awards
In 1869, Casey was awarded the Honorary Degree of Doctor of Laws by Dublin University. He was elected a Fellow of the Royal Society in June, 1875. He was elected to the Royal Irish AcademyRoyal Irish Academy
The Royal Irish Academy , based in Dublin, is an all-Ireland, independent, academic body that promotes study and excellence in the sciences, humanities and social sciences. It is one of Ireland's premier learned societies and cultural institutions and currently has around 420 Members, elected in...
and in 1880 became a member of its council. In 1881 the Academy conferred upon him the much coveted Cunningham Gold Medal. His work was also acknowledged by the Norwegian Government, among others. He was elected a member of the Societe Mathematique de France in 1884 and received the honorary degree of Doctor of Laws from the Royal University of Ireland
Royal University of Ireland
The Royal University of Ireland was founded in accordance with the University Education Act 1879 as an examining and degree-awarding university based on the model of the University of London. A Royal Charter was issued on April 27, 1880 and examinations were opened to candidates irrespective of...
in 1885.
Major works
- On Cubic Transformations (Dublin, 1880)
- A Sequel to the First Six Books of the Elements of Euclid (Dublin, 1881)
- The First Six Books of the Elements of Euclid (Dublin, 1882)
- A Treatise on the Analytic Geometry of the Point, Line, Circle and Conic Sections (Dublin, 1885)
- A Treatise on Elementary Trigonometry (Dublin, 1886)
- A Treatise on Plane Trigonometry containing an account of the Hyperbolic Functions (Dublin, 1888)
- A Treatise on Spherical Geometry (Dublin, 1889).
See also
- 1913 Catholic Encyclopedia article on John Casey
- "James Maher, Chief of the Comeraghs, Mullinahone, 1957, pp 295-299.