Morgan Crofton

Morgan Crofton (* June 27, 1826 in Dublin, † May 13 1915 in Brighton ) was an Irish mathematician.

Crofton was born the son of a Protestant pastor ( he was the successor of the father of George Stokes, who was also a priest in Skreen, County Sligo). Crofton studied at Trinity College in Dublin. As he thought about this time, to go to the Catholic faith ( under the influence of the later Cardinal John Henry Newman in Birmingham), he would not accept him in 1848 offered Fellowship at Trinity College, which was associated with an ordination in the Anglican Church. In 1849 he became professor of theoretical physics (Natural Philosophy) at Queen's College in Galway, but came back in 1853, when he became a Catholic. He then taught at a number of Jesuit schools in France. Later, he was appointed on the recommendation of James Joseph Sylvester at the Royal Military Academy at Woolwich, where he also Sylvester's successor as professor of mathematics in 1870. In 1884 he retired and in 1884 professor at the University College Dublin ( the successor of the Catholic University in Dublin, who had founded Newman), the lectures left but John Casey, came only on tests and continued to live in London. In 1895 he went again to retire.

Crofton worked example on geometry, James Clerk Maxwell's theory of trusses, but is today mainly for his work in geometric probability theory known ( integral geometry ), where Crofton 's formula is named after him. It arose from the observation of Buffon's needle problem ( Crofton "On the theory of local probability", Transactions of the Royal Society, Bd.158, 1868, p.181) and pushes the arc length s of a plane curve by an integral over the number of intersection with a randomized "needle", which is the ( oriented ) unit line, with the distance from the origin P and of the orientation ( angle ) as the parameters from.

It is evenly distributed in terms of position and orientation lines for the normalized density. For undirected lines have been inserted according to a factor of 2. Crofton formulas also headed for the "hit number" of lines on Eilinien and two Eilinien simultaneously.

He also wrote the influential article on probability theory in the 9th edition of the Encyclopedia Britannica from 1885 ( Bd.19, S.768 -788 ).

In 1898 he became an honorary doctorate from Trinity College, Dublin.

Writings

• Lectures on the elements of applied mechanics, 1877
• With E.Kensington Tracts on Mechanics