In Berlin Mitte at address Behrenstrasse 21 is the Bayerische Vertretung, whose functions are described as “… die Aussenstelle der Staatskanzlei in der Bundeshauptstadt,” or “branch office of the Bavarian State Chancellery in the German capital.”
Swiss scientist Leonhard Euler spent some 20 years (1743-1766) in Berlin, living in this very building and working at the Académie Royale des Sciences et Belles-Lettres de Prusse (now, Berlin-Brandenburg Academy of Sciences). Euler’s name is very familiar to anyone who’s encountered and studied mathematics and physics. He is well known for his study and work in the fields of physics, astronomy, and engineering. But for his contributions to notation, functional analysis, number theory, and graph theory, Euler is considered one of the greatest mathematicians in history. Euler departed Berlin in 1766, accepting an invitation from Russia’s Catherine the Great to return to St. Petersburg where he remained for the rest of his life.
Why Euler’s contributions are important
1. Notation by Euler put into common practice and usage, from “The Story of Mathematics”:
2. Euler introduced exponentials and logarithms in his analysis, and he defined the exponential function for complex numbers with relation to trigonometric functions. The Euler formula (complex exponential function) for variable or angle φ is:
Setting φ to numerical constant π produces the Euler identity:
Remarkably simple and powerful, the Euler identity combines in a single elegant equation the mathematics of addition, multiplication, exponentiation, and equality, with the universal constants 0, 1, e, i, π. Practical applications of the Euler formula and Euler identity reach into the fields of biology, chemistry, economics, electrical engineering, and physics.
3. The Euler-Lagrange equation is a result of Lagrange’s solution to the tautochrone curve and Euler’s invention of the calculus of variations. Fundamental in the study of classical mechanics and classic field theory, the Euler-Lagrange equation can be used to reformulate Newton’s laws of motions to a set of generalized coordinates, and to determine the dynamics of a classical field. The (one-dimensional) Euler-Lagrange equation is expressed as the following partial-differential equation:
for Lagrangian, L, equal to the difference between kinetic energy and potential energy; spatial-coordinate x; time t; and speed ẋ. Examples and specific solutions to this equation are found here (pdf), here, and here (pdf).
I made the above photographs on 9 December 2015 with a Canon EOS6D mark1. This post appears on Fotoeins Fotografie at fotoeins DOT com as http://wp.me/p1BIdT-7A0.