Questions tagged [gauss]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
42
votes
2answers
10k views

Did Gauss find the formula for $1+2+3+\ldots+(n-2)+(n-1)+n$ in elementary school?

I heard Gauss's primary school teacher gave some busy-work to his class: to add all the numbers between 1 and 100 up. Gauss immediately wrote 5050. His teacher was shocked, so she told him to add up ...
22
votes
3answers
2k views

How did Gauss become the “the prince of mathematicians”?

Gauss is probably the most famous mathematician today, his face even appears on one of European bills. But he did not have a charismatic personality, like Galois, nor was particularly interested in ...
8
votes
1answer
771 views

Did Gauss say “there have been but three epoch-making mathematicians, Archimedes, Newton and Eisenstein”?

In Wikipedia I found this claim by E.T. Bell in his Men of Mathematics. However in the next paragraph it says that "it is doubtful that Gauss put Eisenstein in the same league as Newton", which makes ...
7
votes
2answers
506 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. ...
7
votes
1answer
268 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 ...
6
votes
1answer
203 views

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 libration. As is ...
6
votes
3answers
204 views

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 ...
6
votes
2answers
541 views

A question on Gauss' “Vicimus GEGAN”

The 43rd entry(Oct. 1796) of Gauss' mathematical diary "Vicimus GEGAN" remained a mystery for a long time. K. R. Biermann found evidence that GEGAN is related the famous arithmetic-geometric mean(AGM) ...
6
votes
1answer
640 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 ...
6
votes
2answers
424 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
votes
1answer
257 views

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 ...
5
votes
2answers
276 views

When did Gauss introduce “Gauss' planetary equations”?

"Gauss' planetary equations" are a set of equations that describe the rate of change of the six elements of a planetary orbit in the presence of a disturbing force. I just intend to ask in which of ...
5
votes
0answers
157 views

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 ...
4
votes
1answer
515 views

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 ...
4
votes
2answers
342 views

What topological ideas did Gauss introduce to his student Möbius?

Recently I found a website with good historical information about the contributions of Gauss to Analysis situs (the old term for topology). The site is in German so I made a Google translate to ...
4
votes
2answers
618 views

Did Gauss know the residues theorem in complex analysis in 1811?

My question refers to Gauss's 1811 letter to Friedrich Bessel, which contains a statement of Cauchy integral theorem. I have access to the letter, but I'm unable to read it. I know that Gauss gives ...
4
votes
1answer
161 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 ...
4
votes
2answers
324 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 ...
4
votes
2answers
336 views

What mathematical techniques Gauss used in order to tessellate the unit disk?

This question is a continuation of my previously posted question: Was Gauss aware of the non-euclidean implications of his work on moduler forms?, and is based on the information given in John ...
4
votes
1answer
559 views

Gauss's anticipation of quaternions and their relation to congruences

Recently i read the article "Hamilton, Rodrigues, Gauss, Quaternions and Rotations: A Historical Reassessment", which can be found freely on the internet. This article is by far the most comprehensive ...
4
votes
2answers
326 views

Question about Gauss's contributions to the theory of electric circuits

This question is a continuation of my previously-posted question: Several questions about Gauss's contributions to electromagnetism. I wrote it after user vonbrand asked me to split my original ...
4
votes
1answer
290 views

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 ...
4
votes
1answer
193 views

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 ...
4
votes
0answers
93 views

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 ...
4
votes
0answers
216 views

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/...
3
votes
1answer
118 views

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 ...
3
votes
1answer
222 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. ...
3
votes
1answer
215 views

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 ...
3
votes
1answer
154 views

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 ...
3
votes
1answer
273 views

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 ...
3
votes
1answer
205 views

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 ...
3
votes
1answer
173 views

What were Gauss's contributions to capillarity?

I am writing a Wikipedia article (in a certain language) in which I intend to include a summary of Carl Friedrich Gauss's contributions to capillarity. I know that Gauss derived the Young-Laplace ...
3
votes
1answer
205 views

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 ...
3
votes
1answer
167 views

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 ...
3
votes
1answer
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 ...
3
votes
2answers
528 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 ...
3
votes
0answers
95 views

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 ...
2
votes
1answer
96 views

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 ...
2
votes
1answer
335 views

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 ...
2
votes
1answer
210 views

What is the modern interpretation of Gauss's “Summatorische Function”?

In Buhler's biography of Gauss (Gauss: A Biographical Study), at the chapter on modular forms and hypergeometric series, he mentions a function that Gauss called "Summatorische Function", which he ...
2
votes
0answers
115 views

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 ...
2
votes
0answers
112 views

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 ...
1
vote
3answers
357 views

What is the purpose of Gauss in his letter to János Bolyai when he mentioned “howling Boeotians”?

I'm wondering what is the purpose of Gauss in his letter to János Bolyai when he mentioned "howling Boeotians"? Is it related to some scientists or philosophers that opposed non-Euclidean geometry? I ...
1
vote
1answer
78 views

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 ...
1
vote
1answer
177 views

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.
1
vote
1answer
135 views

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 ...
1
vote
0answers
112 views

Question about the meaning of an important footnote to entry 109 in Gauss's diary

Entry 109 in Gauss's diary (and the related material in Gauss's Nachlass) is the main subject of David Cox's famous article "The Arithmetic-Geometric mean of Gauss". This entry deals with ...
1
vote
0answers
112 views

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, volume V,...
1
vote
1answer
213 views

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 ...
0
votes
2answers
234 views

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 ...