MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Biographical Vignettes 171
member of the French Academy of Sciences to be elected to every one of its
five sections and he served as its President. In addition, he received many
medals and honors. He died from complications following prostate surgery in
Paris, France, aged 58. Source material for Poincaré is available in [23, 42].
Vignette 28 (Percy Alexander MacMahon: 1854-1929).
Percy MacMahon was born into a military family in Sliema, Malta [144]. In
1871, he entered the Royal Military Academy at Woolwich and studied under
the renowned teacher of physics and Mathematics, Alfred George Greenhill.
He was posted to India in 1873 until he was sent home to England in 1878 to
recover his health. He was appointed Instructor of Mathematics at the Royal
Military Academy in 1882 and held that post until he became Assistant Inspector
at the Arsenal in 1888. In 1891, he took up a new post as Military
Instructor in Electricity at the Royal Artillery College, Woolwich where he
stayed until his retirement from the Army in 1898. He worked on invariants
of binary quadratic forms and his interest in symmetric functions led him to
study partitions of integers and Latin squares. In 1915/1916, he published his
two volume Combinatory Analysis which was the first major book in enumerative
combinatorics and is now considered a classic. The shorter Introduction to
Combinatory Analysis was published in 1920. He also did pioneering work in
Recreational Mathematics and patented several puzzles. His New Mathematical
Pastimes (1921) contains the 24 color triangles introduced in Recreation
17. He was a Fellow of the Royal Society and served as President of the London
Mathematical Society, Section A of the British Association and the Royal Astronomical
Society. He was also the recipient of the Royal Medal, the Sylvester
Medal and the Morgan Medal. He died in Bognor Regis, England, aged 75.
Vignette 29 (Frank Morley: 1860-1937).
Frank Morley was born into a Quaker family in Woodbridge, Suffolk, England
[230, 330]. He studied with Sir George Airy at King’s College, Cambridge,
earning his B.A. in 1884. He then took a job as a school master, teaching
Mathematics at Bath College until 1887. At that time he moved to Haverford
College in Pennsylvania where he taught until 1900, when he became
Chairman of the Mathematics Department at the Johns Hopkins University in
Baltimore, Maryland. He spent the remainder of his career there, supervising
48 doctoral students. He published the book A Treatise on the Theory of Functions
(1893) which was later revised as Introduction to the Theory of Analytic
Functions (1898). He is best known for Morley’s Theorem (see Property 11),
which though discovered in 1899 was not published by him until 1929, but also
loved posing mathematical problems. Over a period of 50 years, he published
more than 60 such problems in Educational Times. Most were of a geometric
nature: “Show that on a chessboard the number of visible squares is 204 while