Questions tagged [gauss]

Carl Friedrich Gauss (1777-1855) was a German mathematician and physicist who worked in number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. His contributions were immense.

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281 views

Calculation of Gauss leading to 18:7 resonance between orbits of Jupiter and Pallas

After Gauss helped relocate Ceres, he studied the orbit of the asteroid Pallas and discovered (1812) that Jupiter and Pallas have an orbital resonance that is nearly equal to 18:7. For instance, using ...
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196 views

What was Gauss's method for solving the "trinomial equation"?

In the second part of his fourth proof of the fundamental theorem of the algebra (published in 1849 [1]), entitled "A contribution to the theory of algebraic equations", Gauss gives a new ...
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524 views

Did Gauss know Jacobi's four squares theorem?

In pp. 283–285 of volume 2 of Dickson's “history of the theory of numbers” appear several formulas of striking similarity: some of them are stated by Gauss (p. 283) and some are stated by Jacobi (p. ...
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296 views

Several questions about Gauss's contributions to electromagnetism

First of all, i appologize if i'm asking too many questions about Gauss (and some will also say "not very interesting questions"); i know i might appear ridiculus - but i really think it's an ...
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530 views

Did Gauss's expression for the differential of the hyperbolic volume of the tetrahedron agree with later results?

My question is mainly about getting explanation to Gauss's third note (note III) in his writing "Zur Astralgeometrie", (see Cubierung der Tetraeder, pages 228-229), and about placing it in the right ...
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245 views

Question about Hermite's 1858 solution to the quintic equation using elliptic modular functions and it's relation to Gauss' and Jacobi's work

The general quintic equation cannot be solved by radicals and is shown in a landmark and far reaching work of Galois from 1832, which became a template of modern Group theory and Galois theory. ...
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442 views

Did Gauss formulate, or at least know of, the full essence of the Gauss-Bonnet Theorem?

I know that a special case of the Bonnet theorem, called the Theorema Elegantissimum, was proved by Gauss in his 1827 treatise on differential geometry. This was a theorem that dealt with the ...
6
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1answer
643 views

Meaning of passages by Gauss on the "convergence of expansions (in infinite series) of the (elliptical) equation of the center"?

Yesterday I took my time to look again into Schlesinger's essay on Gauss's contributions to analysis, and I found something new I didn't know about (so it caught my eye) in the last subsection of the ...
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What was Gauss's theoretical work related to his invention of the "Double-Gauss lens"?

Gauss's contributions (Dioptriche Untersuchungen, 1840) to the "classical" optical theory (Gaussian optics, i.e calculations made under the paraxial approximation) are well known, but long before he ...
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335 views

Was Gauss aware of the non-euclidean implications of his work on moduler forms?

Until recently, i thought that the first to observe the connection between modular forms and the hyperbolic plane (a model of non-euclidean geometry) was Felix Klein. But in the last week i read the ...