Questions tagged [euler]
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43 questions
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Where/when/how did "Euler angles" originate?
I think it's fair to say that the modern understanding of the phrase "Euler angles" is essentially a sequence of three angles representing three successive rotations about a set of ...
- 201
6
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1
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$a^b=b^a$ (very nice symmetric equation)
I am just interested in knowing if Euler ever solved this problem: $a^b=b^a$? ($a \ne b$).
I discovered it when I was a kid, as a 12 year-old, and solved it. It was in 1989.
I was asking professors ...
2
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0
answers
104
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Do we know what books Euler read/worked through while studying with Johann Bernoulli at the University of Basel?
I've been reading Gautschi's brief biographical review of Euler in which he quotes Euler's autobiography (as provided in Fellmann's biography of Euler) a passage about Euler's study with Johann ...
- 223
6
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1
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Did Euler guess the Basel problem’s solution to be $\frac{\pi^2}{6}$?
(posted & answered, then closed in MSE)
I've been interested in the Basel problem and its famous solution
$$
\sum_{n=1}^{\infty}{\frac{1}{n^2}} = \frac{\pi^2}{6}.
$$
Recently I saw this video ...
- 163
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0
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Was Euler aware of the general form of the characterization of primes of the form $p=x^2+ny^2$ for arbitrary $n>0$?
If $n$ is a positive integer then there is a monic irreducible polynomial $f(x)$ such that if $p$ is an odd prime not dividing $n$ nor the discriminant of $f$ then
$$
p=x^2+ny^2\iff \left(\frac{-n}{p}\...
- 191
3
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0
answers
318
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I would like to read about Euler's view on negative numbers
So, I've been over fixated on negative numbers lately. I'm coming to the conclusion that, mathematics is usually progressed if it is "useful". The more "useful" a mathematical ...
- 113
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0
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Need a reference for Euler's velocity initial condition for the wave equation
In DOI: 10.4236/ahs.2020.94019 235 Advances in Historical Studies, p.234
D’Alembert and the Wave Equation: Its Disputes and Controversies, or https://www.scirp.org/pdf/ahs_2020112716312281.pdf p.6 of ...
- 173
3
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2
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734
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Did Euler know Ancient Greek?
In a previous question on this website: What was Euler's first language?,
Alexandre Eremenko wrote the following about Leonard Euler:
There is little doubt that he also learnt French in his ...
user18960
1
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1
answer
246
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Did any mathematicians of the time (the 17th Century) try out an intermediary between Bernoulli's and Nieuwentijdt’s infinitesimals?
In §4 of the Stanford Encyclopedia of Philosophy article on continuity and infinitesimals, the author (John L. Bell) mentions that:
... Johann Bernoulli (1667–1748) [in a] letter of his to Leibniz ...
- 111
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0
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17th or 18th century use of the continued fraction expansion of $(1 + \sqrt D)/2$ to solve the diophantine equation $x^2 - D y^2 = 4$
Can someone please provide an early reference to the use of the continued fraction expansion of $\frac{1+\sqrt D}2$ to solve the Diophantine equation $x^2 - D y^2 = 4$ for a positive integer $D$ ...
5
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1
answer
329
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Who first called $\mathrm e$ "Euler's number"?
Euler is usually credited with denoting this number with the letter $\mathrm e$. But
It seems unlikely that Euler chose the letter because it is the initial of his own name, as occasionally been ...
user18522
8
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4
answers
4k
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Have all of Euler's works been translated?
I am interested in reading Euler's works.
The Euler Archive contains some translated works but not all of them. I am just checking here to see if anyone know a complete translation of all of Euler's ...
- 449
1
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0
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215
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When and why Cantor-Hume principle was universally adopted in set theory instead of Euclid's principle?
In this answer and the comments Joel David Hamkins talks about a conflict between Cantor-Hume principle and Euclid's principle. He writes:
This principle [Cantor-Hume] is often defended as a ...
- 702
24
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1
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Euler: “A baby on his lap, a cat on his back — that’s how he wrote his immortal works” (origin?)
Euler was a non-confrontational and deeply religious person. He was kind and could get on well with anyone. He worked under any circumstances and in any environment: “A baby on his lap, a cat on his ...
- 343
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In which work did Euler invent the Euler Substitutions for a quadratic composed into a radical?
A famous technique in the modification of integrands is the set of “euler substitutions” that provide substitutions for the structure
$$\sqrt{ax^2 +bx+c}$$
That is a fairly common occurence in ...
- 449