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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Was the "Gauss word realization problem" a kind of unknotting problem?
In Moritz Epple's article "Geometric Aspects in the Development of Knot Theory", Epple writes the following:
It has been suggested that one of the earliest tools of combinatorial knot ...
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Implications of several unpublished "binomial congruences" of Gauss
In article 23 of his first memoir on biquadratic residues, Gauss gave the first example of a binomial-type congruence, which is apparently a quite "deep" result - many authors relate it to ...
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Gauss' Theorema Egregium
I am looking for the historical context in which Gauss established its famous Theorema Egregium. Was Gauss studying map projections (a nowadays popular application of the theorem)? Any references are ...
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Autistic Assistant of Gauss used to check Primality
The Arora-Barak book on complexity contains the following sentence with the following footnote, page 128:
In primality testing, we are given an integer N and wish to determine
whether or not it is ...
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Question on Gauss's geometric interpretation of "spherical functions"
In the physics chapter of his biography of Gauss, W.K. Buhler writes the following:
Expansions into series are frequent and important in potential theory. So it does not come as a surprise that ...
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Entry 97 in Gauss's diary and the status of "lunar parallax" in the late 18th century
P.539-542 of volume 10-1 of Gauss's werke include entry 97 in Gauss's diary:
I have found new exact formulas for the parallax of the moon.
as well as the formulas themselves (which were rather found ...
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Motivating several of Gauss's suggestions for prize problems in the years 1830, 1834
P. 220-221 of volume 12 of Gauss's werke contain a complete list of the prize problems which Gauss suggested to the Goettingen university in the years 1830, 1834, 1842 and 1849. Those prize problems ...
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What was Gauss's algorithmic method to solve a certain "nearest neighbour search" problem in multi-dimensional euclidean space?
In his 1829 paper on a new formulation of mechanics, Gauss presented his principle of least constraint, which parallels previous formulations of analytical mechanics and provides a new point of view ...
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Non-Euclidean geometry: motivations to develop it at the times of Gauss?
I'm making a historical research on the origins of differential geometry, starting with non-Euclidean geometry introduced by Gauss. Reading different historical accounts, what I don't understand is ...
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How did Gauss come up with his law?
Why did it seem at the time of Gauss that the quantity we get by multiplication of electric field with the area would have some value to it? That is what was the motivation for Gauss to find the flux ...
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In orbital determination of celestial bodies, why did the case of parabolic or nearly-parabolic orbits require separate development?
In Buhler's biography of Gauss, who made huge contributions to the development of efficient orbital determination methods in his Theoria Motus (1809), the following information is mentioned:
The ...
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How to give a meaningful interpretation to Gauss's notion of "oriented area" of self-intersecting geodesic polygons?
Gauss's notion of "oriented area" of figures characterizes the notion of two-dimensional content in a way that enables self-intersecting geodesic polygons (the term "geodesic" ...
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is there an online archive of all of Gauss' works?
I found a gem called the Euler Archive and I was looking for similar easy access to Gauss' works but I couldn't find it via google searches so I beseech thee
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Explanation request for the terminology and notation employed by Gauss in his major 1843/6 treatise on Geodesy
Background:
In his 1827 treatise on differential geometry, Gauss in his "theorema egregium" proved that the curvature of a surface is an intrinsic invariant; it doesn't change under ...
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What is the significance of Gauss-Weierstrass's derivation of "Al functions"?
In a fragment entitled "inversion of the elliptic integral of the first genus" (Gauss's werke, volume 8, p. 96-97), Gauss inverts the general elliptic integral of the first kind: he writes $\...
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Reference request for Gauss's original discovery of the special property of the $j$ function
In Interchapter VII of his biography of Gauss, W.K. Buhler describes Gauss's discovery of one of the important properties that characterize the $j$ invariant (Klein's absolute invariant; Gauss called ...
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Did the formation of Differential Geometry come before Differential Topology/ Topology in general?
I’m pretty interested in the history of mathematics, and it has always been my belief that the great pioneers of Differential Geometry were Gauss and Riemann, and the father of topology was mostly ...
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Explanation of the main points in Gauss's resultant calculus
After he read Mobius's 1827 treatise on the "barycentric calculus" (according to Gauss's own testimony, he read this treatise only in 1843), Gauss wrote down several unpublished notes on ...
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Authenticity of Gauss's Quote "If others reflect on mathematical truths as deeply as I..."
in Gauss's Section in 'The World of Mathematics' Gauss is said to have declared that :
If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my ...
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Any historical work on the distribution of prime gaps?
I am looking to see whether historic mathematicians did any work to explain the slightly unexpected distribution of prime gaps?
I would have expected Gauss, who studied lists of primes and proposed a ...
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What was the influence of Gauss on the understanding of the importance of non-Euclidean geometry?
As is known, Gauss came to similar conclusions as Lobachevskii in the problem of fifth postulate, but I don't know whether Gauss had any impact to the contemporaries in that story. Can anybody ...
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Explanation of a remark of Gauss on exceptional cases of conformal mappings
In his letter to Hansen (december 11, 1825), Gauss responds to several questions asked by Hansen about his recent 1822 publication ("A general solution to the problem of mapping the parts of a ...
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A quote attributed to Gauss
A version of this question first appeared in MathOverflow but did not receive satisfactory answers.
This quote is often attributed to Gauss:
Die Mathematik ist die Königin der Wissenschaften, und ...
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Reference request for some fragments of Gauss with dubious origin
Gauss's results on the interconnection between the different values of the arithmetic-geometric mean of two complex numbers as recorded in his private notebooks led him to introduce foundational ...
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Did the 1800 Gregorian Lunar Correction Motivate Gauss' Computus Algorithm?
When the Gregorian calendar was implemented in 1582, one of its adjustments was the lunar correction---to increase the epact by 1 eight times within a span of 2500 years; specifically, seven times ...
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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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Question about the significance of "Gauss-Legendre quadrature"
I want to understand why, according to several sources, Gauss's discovery of Gaussian quadrature in his 1814 article was "the most significant event of the 19th century in the field of numerical ...
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Meaning of certain identities of Gauss on theta functions
Volume 3 of Gauss's werke contains an unpublished treatise with the title "Theory of new transcendents" (p.433-481 of the same volume), whose writing is dated, according to the editor ...
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What was the optical problem discussed and solved by Gauss in his 1831 letter to Brandes?
Volume 5 of Gauss's works contains a section which includes "Essays on various objects in mathematical physics". Just to emphasize the importance of this section, i'll mention that it ...
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Who discovered the thin lens equation $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$?
According to Weisstein's webpage it was Halley in 1693 (quoting Steinhaus); but I've also seen it attributed to Cotes, Huygens, even Gauss (eg Britannica). Wikipedia's History of Optics does not give ...
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Interpretation of a short note of Gauss on the resolution of a special system of inhomogeneous linear equations by roots of unity
My question refers to a 2-pages fragment of Gauss, entitled: "Note on the resolution of a special system of linear equations", which is found on pages 30-31 of volume 8 of his works. In this ...
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Were the kilogram, the grave, etc. meant to be units of weight, units of mass, or was it ambiguous at the time?
It is sometimes stated that the early metric units of 'weight' really were meant to be exactly that: units of weight (i.e. force), not mass. However, is that really so? In fact, did the people ...
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Do you know about this anecdote or its source where the mother reads out the letter to Gauss and made him Gauss, the mathematician?
I remember my brother telling me an anecdote about Carl F. Gauss three-four years ago, I want to know if anybody here also know about it, or can provide the source of it. The anecdote goes like this
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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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Were Gauss's 1846 remarks on the distinction between right and left related to orientability of surfaces?
Recently i was striked by a quotation of Gauss from a letter to his student Gerling from the date June 23, 1846. This letter states in very concise words that the distinction between right-handed and ...
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What are the context and motivation for Gauss's study of the "Pothenot problem"?
My question refers to p.307-335 of volume 8 of Gauss's werke, which are part of a section of volume 8 which deals with Gauss's applications of complex numbers for geometry. The pages mentioned are ...
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Gauss on philosophers
Carl Friedrich Gauss said:
When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.
On one occasion I read that supposedly ...
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How did Gauss and Lagrange derive Gauss law of Electrostatics
On Wikipedia, these two pages are mentioned :Lagrange and Gauss
however I am an English speaker and can not comprehend any of the one, can someone provide the translated pages or shortly their line of ...
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What is the modern context of Gauss's work on triangles with integer sides and circumradius?
In chapter V of volume 2 of Dickson's "History of the theory of numbers" (p.191-195), which collects results on "rational" triangles (triangles with integer side lengths), apear several results on the ...
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What was the "libration of Pallas" that Gauss studied, when Pallas is not a moon of Jupiter?
This question is a request for general explanation of an astronomical phenomenon known as "Pallas libration", and isn't much about the details of Gauss's mathematical model of this ...
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Two questions about Gauss's contributions to capillarity and the calculus of variations
In the last page of the abstract of Gauss's paper on capillarity "Principia generalia theoriae figurae fluidorum in statu aequilibrii" (1829), the author (who is he?) mentions (Gauss's werke,...
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Where in Gauss's nachlass apears his sketch of a geometric proof for the biquadratic reciprocity law?
According to p.200-202 of the book "Reciprocity Laws: From Euler to Eisenstein" by Franz Lemmermeyer, there are two proofs for the biquadratic reciprocity law in Gauss's nachlass: one is a cyclotomic ...
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Several questions about Gauss's contributions to observational astronomy
I just want to check if anyone has additional information about a private astronomical research begun by Gauss in 1819, which dealt with the "movements of the solar system" in the galaxy (motion of ...
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Entry in Gauss' Mathematisches Tagebuch (Mathematical Diary)
Does someone have a reference or further explanation on Gauß' entry from May 24, 1796 in his mathematical diary (Mathematisches Tagebuch, full scan available via https://gdz.sub.uni-goettingen.de/id/...
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Where in Gauss's nachlass did he pose the problem of connectedness of a surface?
On p.98 of the book "Mathematics of the 19th Century: Geometry, Analytic Function Theory", the authors mention a note written by Gauss in 1840:
In 1840 Gauss wrote a note in which he introduced the ...
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Origin of Gauss-Newton method
The Gauss-Newton method can be derived from Newton's method, but I am unable to see how Gauss was linked with this method. It seems unlikely that he himself worked on the method, but I am at a loss.
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Explanation of Gauss's late fragments dealing with "the conformal image of the ellipse"
My question refers to some not very well known fragments of Gauss that treat the problem of finding a conformal mapping (angle-preserving mapping) in the complex plane from the interior of the ellipse ...
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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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Several questions about Gauss's mathematical conception of braids
I'm trying to figure out several things about Gauss's thoughts concerning a certain four-strand braid. The reference my questions are based on is mainly Moritz Epple's excellent article "orbits ...
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History of the Gauss Circle Problem
The Gauss Circle Problem: find the number of integer lattice points inside a circle.
My question is: why was Gauss studying this problem? Was it just math for math's sake, or was this a part of a ...
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