## Berlin Mitte ‘Math’: where Euler lived for 23 years

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

### Where some math & physics get prominent

**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

Substituting the numerical constant π for variable φ yields 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 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).

• Euler Archive, by MMA in English

• “300 Jahre Leonhard Euler” (300 Years of Euler), by BBAW in German

I made the above photographs on 9 December 2015. I used the CodeCogs online LaTeX-to-html equation editor. This post appears on Fotoeins Fotografie at fotoeins.com as http://wp.me/p1BIdT-7A0.

## 8 Responses to “Berlin Mitte ‘Math’: where Euler lived for 23 years”

Have you read the book ” Das Geheimnis der Eulerischen Formel” ?

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Hi, Cornelia. No, I have not!

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Hi, Cornelia. Mir ist interessant: hab’s Online-Review von “Der Speigel” gefunden (http://goo.gl/UmG0mt). Aber das Buch heisst “The Housekeeper and the Professor” auf Englisch; ich suche nun ja einen. Also, möcht’ ich ganz lieber den deutsche Titel. 😉

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Ich habe das Buch in Deutsch, und kann es dir gerne schicken, in welchem Land lebst du? Lass ich wissen, I’ll be happy to mail it to you. You can send me your address to my email corneliaphotography@cox.net

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Thank you for your offer, Cornelia, but you don’t have to do that, as I’ve reserved a copy of the book in English from our city library.

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Cornelia, I just finished Yoko Ogawa’s book “The Housekeeper and the Professor” (marketed and sold as “Das Geheimnis der Eulerischen Formel” in Germany). It is frankly one of the most beautiful pieces of writing I’ve read in a long time, which included remarkable themes like the fragility of memory, people, and relationships, with themes that speak

verywell with me like mathematics and baseball. Despite not knowing a word of Japanese, I knew about halfway I wanted to “step inside” the book and meet these characters as if they were real, but knowing that the mere “act” of trying meet them would almost seem like a rude interruption. Thanks for the tip/recommendation!LikeLiked by 1 person

Thank you for sharing your thoughts on this book and can’t agree more with you. Once I started reading I couldn’t put the book down, I was really amazed by the way she describes the characters. I should look into her other books. I am glad that you loved it that. Unfortunately I forgot your first name, sorry, sometimes I have memory blocks.

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Fotoeins, I am sorry I can’t remember your first name, sometimes I have “memory blocks”. Thank you so much for sharing your thoughts on this book . Once I started reading I couldn’t put it down. The way she describes the characters is just amazing. I should look into her other books.My friend in Germany ( a book seller as well) had send me once an interview of a German writer with Yoko Ogawa and interestingly I found her book in a book store at the airport in Munich. The author lives a pretty secluded spiritual live in Japan. I am glad that you loved it that much.

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