2008/01/07 by Leonhard Euler, Euler, Leonhard
Engineering · Mathematics · #01A50 #49-03 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications #math.CA #math.HO #msc:01A50 #msc:49-03
paper · pdf · doi:10.48550/arxiv.0801.0897
10 pages; E727 in the Enestrom index
arxiv created 2008/01/07 · openalex publication_date 2008/01/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
E727 in the Enestrom index. This is a translation from the Latin original "Accuratior evolutio problematis de linea brevissima in superficie quacunque ducenda" (1779). Given a surface pdx+qdy+rdz=0, Euler wants to develop equations that give the geodesics on this surface. I am new to the calculus of variations, so it is not clear to me what steps follow from results that are previously known (like the Euler-Lagrange equation in the calculations) and what steps follow from earlier in this paper. I would appreciate comments from any readers who are familiar with calculus of variations.