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Is there an English translation of "Wie sich entscheiden lässt, ob zwei gegebene krumme Flächen auf einander abwickelbar sind oder nicht..." by Ferdinand Minding, Journal für die reine und angewandte Mathematik, (page(s) 370 - 387) Berlin; 1839

Or is there a simpler or more recent proof of the same theorem? (This states that isometric triangles on surfaces with the same Gaussian curvature are congruent, and vv if I understand the theorem correctly)

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    $\begingroup$ Assuming it's no coincidence that you have a Dutch name, you certainly can read German without needing to look in a dictionary too much; just try;-) The harder part will be to convert the text to modern terminology, but this equally applies to other languages. $\endgroup$ – Dima Pasechnik Oct 16 '14 at 6:44
  • $\begingroup$ Can you state the theorem you want more precisely ? In particular the distinction between isometric and congruent. $\endgroup$ – Thomas Richard Oct 17 '14 at 8:12
  • $\begingroup$ @ThomasRichard sorry as stated is my interpretation of the theorem, (maybe a bit simplified) : isometric triangles == triangles with the same distances between the vertices (angles do not have to be equal) , congruent triangles == triangles that are isometric triangles and where also the angles are equal) Minding describebes it as "ob zwei gegebene krumme flachen die auf einander abwickelbar sind" (rough translation: if two given curved surfaces are congruent) $\endgroup$ – Willemien Oct 18 '14 at 0:18
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Is there a simpler or more recent proof of the same theorem? The theorem is given as an exercise with solution (number 1.2) in this differential geometry course by Michael Eichmair at the ETH.

You can also find a proof on page 292 of A New Approach to Differential Geometry using Clifford's Geometric Algebra by John Snygg, and on page 282 of Differential Geometry by Erwin Kreyszig.

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  • $\begingroup$ I offer by bounty and upvote to thi proof (not the one with all the up votes (I don't read russian) $\endgroup$ – Willemien Oct 21 '14 at 18:41
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Is there a translation of Minding's paper?" Well, yes, there is one from 1956 in the book Об основаниях геометрии. Сборник классических работ по геометрии Лобачевского и развитию её идей. You can download it here, Minding's paper is on pages 166-167.

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    $\begingroup$ An English translation? $\endgroup$ – Todd Trimble Oct 13 '14 at 12:14
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    $\begingroup$ certainly not, Russian. $\endgroup$ – Carlo Beenakker Oct 13 '14 at 12:28
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    $\begingroup$ i would like an english translation (thids getting from the rain in to a ocean , my German is better than my Russian) $\endgroup$ – Willemien Oct 13 '14 at 12:33
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    $\begingroup$ OK, I edited your question accordingly, but will just leave this answer, it might be of use to some of our Russian friends. $\endgroup$ – Carlo Beenakker Oct 13 '14 at 12:38

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