MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Biographical Vignettes 161
was buried in Westminster Abbey. Chapter 1 noted how Newton patterned his
Principia after Euclid’s The Elements and alluded to his alchemical activities.
Source material for Newton is available in [42, 221, 227, 287, 297].
Vignette 17 (Leonhard Euler: 1707-1783).
Leonhard Euler was born in Basel, Switzerland and entered the University
of Basel at age 14 where he received private instruction in Mathematics from
the eminent Mathematician Johann Bernoulli [102]. He received his Master
of Philosophy in 1723 with a dissertation comparing the philosophies of
Descartes and Newton. In 1726, he completed his Ph.D. with a dissertation on
the propagation of sound and published his first paper on isochronous curves
in a resisting medium. In 1727, he published another paper on reciprocal
trajectories [265, pp. 6-7] and he also won second place in the Grand Prize
competition of the Paris Academy for his essay on the optimal placement of
masts on a ship. He subsequently won first prize twelve times in his career.
Also in 1727, he wrote a classic paper in acoustics and accepted a position in
the mathematical-physical section of the St. Petersburg Academy of Sciences
where he was a colleague of Daniel Bernoulli, son of Euler’s teacher in Basel.
During this first period in St. Petersburg, his research was focused on number
theory, differential equations, calculus of variations and rational mechanics. In
1736-37, he published his book Mechanica which presented Newtonian dynamics
in the form of mathematical analysis and, in 1739, he laid a mathematical
foundation for music. In 1741, he moved to the Berlin Academy. During the
twenty five years that he spent in Berlin, he wrote 380 articles and published
books on calculus of variations, the calculation of planetary orbits, artillery
and ballistics, analysis, shipbuilding and navigation, the motion of the moon,
lectures on differential calculus and a popular scientific publication, Letters
to a Princess of Germany. In 1766, he returned to St. Petersburg where he
spent the rest of his life. Although he lost his sight, more than half of his total
works date to this period, primarily in optics, algebra and lunar motion, and
also an important work on insurance. To Euler, we owe the notation f(x), e,
i, π, Σ for sums and ∆ n y for finite differences. He solved the Basel Problem
Σ(1/n 2 ) = π 2 /6, proved the connection between the zeta function and the sequence
of prime numbers, proved Fermat’s Last Theorem for n = 3, and gave
the formula e ıθ = cosθ +ı·sin θ together with its special case e ıπ +1 = 0. The
list of his important discoveries that I have not included is even longer! As
Laplace advised, “Read Euler, read Euler, he is the master of us all.”. Euler
was the most prolific Mathematician of all time with his collected works filling
between 60-80 quarto volumes. See Chapter 1 for a description of Euler’s role
in the discovery of the Polyhedral Formula, Property 28 for the definition of
the Euler line, Property 47 for the statement of Euler’s inequality and Recreation
25 for his investigation of the Knight’s Tour. He has been featured on the