RE: https://skyjake.fi/@lagrange/116231863960491740

Now Garvalf's music can be played correctly on the #geminiprotocol with #Lagrange for #Android

gemini://garvalf.ortie.org/musiques

Joseph-Louis Lagrange (1736–1813) found mathematical beauty in many of the fields in which he worked. Here I present some examples from solid geometry.

He considered beautiful Albert Girard’s (1595–1632) theorem relating the area and the angles of a spherical triangle:

The area of a triangle ABC on the surface of a unit sphere is A + B + C − π.

Jean-Étienne Montucla (1725–99) had earlier called the result ‘very elegant’, but had complained that Girard had proved it in a ‘quite laborious and obscure’ fashion. Lagrange thought John Wallis’s (1616–1703) proof was beautiful.

Another result that Lagrange admired was the following:

In any stereographic projection of a sphere onto a plane, any circle on the sphere that does not pass through the point of projection is projected to a circle on the plane (see attached image).

Hence to find the image of such a circle under projection it suffices to find the images of three distinct points on the circle. This fact Lagrange thought a ‘beautiful property of the stereographic projection’.

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#Lagrange #geometry #SphericalGeometry #SolidGeometry #Montucla #MathematicalBeauty #elegance

Antes de nada, bienvenidos y bienvenidas a la Geminisfera.

He reorganizado mi cápsula de Gemini, incluido el gemlog. A partir de hoy solo publicaré mi blog (ahora gemlog) en el protocolo Gemini.

Si queréis, podéis visitar mi cápsula directamente a través del navegador Lagrange (https://gmi.skyjake.fi/lagrange/) o, en el terminal, a través de algún navegador tipo Amfora (https://github.com/makew0rld/amfora).

La dirección original de La Cápsula de un Absolute Beginner es esta:

gemini://abslutebeginner.flounder.online/

Si, por lo contrario, no queréis visitar la versión original de mi gemlog, podéis hacerlo sustituyendo "gemini://" por "https://" en la dirección que os he anotado arriba.

Es mi granito de arena para crear una internet más sencilla y más justa.

Ya no volveré a escribir en la instancia de Writefreely Sopa de Letras (https://sopadeletras.club). Agradezco mucho a sus gestores y mantenedores que me dieran en su momento un pequeño espacio y la posibilidad de publicar un blog con ellos. Y, de paso, les aconsejo a todos y a todas que usen servicios como Writefreely, si es que no se quieren venir a la Geminisfera, lo cual les aconsejo aún más.

#protocolGemini #Lagrange #Amfora #blog #gemlog #cápsula #Geminisfera

Results ranging from visualizable theorems of solid geometry to abstract propositions of analysis were called beautiful by Leonhard Euler (1707–83). For instance, he thought beautiful the following result:

If an elliptical cylinder is cut by any plane at an angle θ, then the ratio of the product of the principal axes of the section and of the product of the principal axes of the base is 1:cos θ (see attached image).

Aesthetic concerns seem to have been part of what drew Euler to number theory. Christian Goldbach (1690–1764) persuaded him to take an interest in the subject and to make a serious study of Fermat's work. His attention was drawn by the theorem:

Every natural number can be expressed as a sum of four squares.

With presumably deliberate understatement, Euler described it as a ‘not inelegant theorem’. The result remained unproven in Euler's time, and the first proof was given by Joseph-Louis Lagrange (1736–1813), becoming known as ‘Lagrange’s four-square theorem’.

Thus, for Euler, *unproven* conjectures could have aesthetic value. And so he judged another well-known then-unproven result of Fermat:

‘In Fermat there is another very beautiful theorem for which he claims to have found a proof. […] the formula $a^n + b^n = c^n$ is impossible whenever $n > 2$’

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[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#Euler #Fermat #Goldbach #Lagrange #FermatsLastTheorem #MathematicalBeauty

Lectures du jour :

“Don’t kill my pretty #RSS feed (#XSLT)” :
https://justinjackson.ca/xslt

“#Lagrange in the Apple App Store” :
gemini://skyjake.fi/gemlog/2026-02_lagrange-in-app-store.gmi

#Gemini #GeminiProtocol #notGoogleGemini