MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Biographical Vignettes 163
infinity. He also studied the integration of differential equations and fluid mechanics
where he introduced the Lagrangian function. In 1764, he submitted
a prize essay to the French Academy of Sciences on the libration of the moon
containing an explanation as to why the same face is always turned towards
Earth which utilized the Principle of Virtual Work and the idea of generalized
equations of motion. In 1766, Lagrange succeeded Euler as the Director of
Mathematics at the Berlin Academy where he stayed until 1787. During the
intervening 20 years, he published a steady stream of top quality papers and
regularly won the prize from the Académie des Sciences in Paris. These papers
covered astronomy, stability of the solar system, mechanics, dynamics, fluid
mechanics, probability and the foundation of calculus. His work on number
theory in Berlin included the Four Squares Theorem and Wilson’s Theorem
(n is prime if and only if (n − 1)! + 1 is divisible by n). He also made a
fundamental investigation of why equations of degree up to 4 can be solved
by radicals and studied permutations of their roots which was a first step in
the development of group theory. However, his greatest achievement in Berlin
was the preparation of his monumental work Traité de mécanique analytique
(1788) which presented from a unified perspective the various principles of mechanics,
demonstrating their connections and mutual dependence. This work
transformed mechanics into a branch of mathematical analysis. In 1787, he
left Berlin to accept a non-teaching post at the Académie des Sciences in Paris
where he stayed for the rest of his career. He was a member of the committee to
standardize weights and measures that recommended the adoption of the metric
system and served on the Bureau des Longitudes which was charged with
the improvement of navigation, the standardization of time-keeping, geodesy
and astronomical observation. His move to Paris signalled a marked decline
in his mathematical productivity with his single notable achievement being
his work on polynomial interpolation. See Property 39 for a description of
his contribution to the Polygonal Number Theorem and Applications 7&8 for
a summary of his research on the Three-Body Problem. He died and was
buried in the Panthéon in Paris, aged 77, before he could finish a thorough
revision of Mécanique analytique. Source material for Lagrange is available in
[23, 42, 297].
Vignette 20 (Johann Karl Friedrich Gauss: 1777-1855).
Karl Friedrich Gauss, Princeps mathematicorum, was born to poor workingclass
parents in Braunschweig in the Electorate of Brunswick-Lüneburg of the
Holy Roman Empire now part of Lower Saxony, Germany [36, 90, 160]. He
was a child prodigy, correcting his father’s financial calculations at age 3 and
discovering the sum of an arithmetic series in primary school. His intellectual
abilities attracted the attention and financial support of the Duke of Braunschweig,
who sent him to the Collegium Carolinum (now Technische Univer-