A more accurate treatment of the problem of drawing the shortest line on a surface

dc.creatorEuler, Leonhard
dc.date2008-01-07
dc.date.accessioned2026-07-07T08:52:54Z
dc.date.available2026-07-07T08:52:54Z
dc.descriptionE727 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.
dc.description10 pages; E727 in the Enestrom index
dc.identifierhttps://arxiv.org/abs/0801.0897
dc.identifierhttp://arxiv.org/abs/0801.0897
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145439
dc.subjectHistory and Overview
dc.subjectClassical Analysis and ODEs
dc.subject01A50; 49-03
dc.titleA more accurate treatment of the problem of drawing the shortest line on a surface
dc.typetext

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