Questions tagged [euler]

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Where did Euler proof 'his' theorem on homogeneous functions?

Where in Eulers writings could I find a proof of his homogeneous function theorem: $y$ is a homogeneous function of degree $k$ in $x_1,\ldots,x_n$ iff $ky = \sum_{i=1}^n x_i\frac{\partial y}{\partial ...
2
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0answers
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Any idea on how Lagrange came up with similar functions concept in (proto)group theory?

Lagrange defines "similar functions" as functions of the roots of an equation where they change values only at the same kind of permutations of the roots. What's a possible predecessor of the idea of ...
1
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0answers
80 views

Where did Euler derive the wave equation in 3d?

Wikipedia claims that Euler was the first do derive the wave equation in 3d. In which of his writings can I find this?
9
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1answer
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Seven bridges of Königsberg - did people know that it was impossible? [duplicate]

I'm not sure if this is the most suitable site for the question. Please feel free to modify or move my post! I have heard that people really walked a lot in Königsberg, trying to solve that seven ...
6
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1answer
106 views

Euler's Derivation of Euler's Method for ODEs

I am looking for an English translation of Euler's derivation of Euler's method for ODEs, namely the update $$ y_{n+1} = y_n + h f(y_n, t_n) $$ What motivated Euler to consider this problem, and how ...
6
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1answer
237 views

What's that on Euler's head? Does the head covering shown in Emanuel Handmann 1753 painting signify scholarship?

This may be borderline off-topic but this is the only place that I can think of ask this particular question. I've always seen images of Leonhard Euler with a "hat" or head covering that is ...
3
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1answer
136 views

Clairaut's proposed correction (reported as “D'Alembert's, Clairaut's and Euler's corrections”) to the Newtonian inverse-square law of gravity

From A.P. Yushkevich, "Leonhard Euler, his life and work", in "Development of Leonhard Euler's ideas and contemporary science", Nauka, Moscow, 1988, 15--46 (translation from Russian is mine): "One ...