MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

162 Biographical Vignettes
Swiss 10-franc banknote and on numerous Swiss, German and Russian stamps.
As part of their Tercentenary Euler Celebration, the Mathematical Association
of America published a five volume tribute [265, 89, 266, 27, 32]. He died
in St. Petersburg, Russia, aged 76. Source material for Euler is available in
[42, 287, 297].
Vignette 18 (Gian Francesco Malfatti: 1731-1807).
Gian Francesco Malfatti was born in Ala, Trento, Italy but studied at
the College of San Francesco Saverio in Bologna under Francesco Maria Zanotti,
Gabriele Manfredi and Vincenzo Riccati (Father of Hyperbolic Functions)
[144]. He then went to Ferrara in 1754, where he founded a school of Mathematics
and physics. In 1771, when the University of Ferrara was reestablished,
he was appointed Professor of Mathematics, a position he held for approximately
thirty years. In 1770, he worked on the solution of the quintic equation
where he introduced the Malfatti resolvent. In 1781, he demonstrated that
the lemniscate has the property that a point mass moving on it under gravity
goes along any arc of the curve in the same time as it traverses the subtending
chord. In 1802 he gave the first, brilliant solution of the problem which bears
his name: Describe in a triangle three circles that are mutually tangent, each
of which touches two sides of the triangle (see Property 70 in Chapter 2). He
also made fundamental contributions to probability, mechanics, combinatorial
analysis and to the theory of finite difference equations. He died in Ferrara,
aged 76.
Vignette 19 (Joseph-Louis Lagrange: 1736-1813).
Joseph-Louis Lagrange was born in Turin, Italy and educated at the College
of Turin where he showed little interest in Mathematics until reading,
at age seventeen, a paper by Edmond Halley on the use of algebra in optics
[151]. He then devoted himself to the study of Mathematics. Although he
was essentially self-taught and did not have the benefit of studying with leading
Mathematicians, he was made a Professor of Mathematics at the Royal
Artillery School in Turin at age nineteen. His first major work was on the
tautochrone (the curve on which a particle will always arrive at a fixed point
in the same time independent of its initial position) where he discovered a
method for extremizing functionals which became one of the cornerstones of
calculus of variations. In 1757, Lagrange was one of the founding members
of what was to become the Royal Academy of Sciences in Turin. Over the
next few years, he published diverse papers in its transactions on calculus of
variations (including Lagrange multipliers), calculus of probabilities and foundations
of mechanics based upon the Principle of Least Action. He made a
major study of the propagation of sound where he investigated the vibrating
string using a discrete mass model with the number of masses approaching