From: nospam@de-ster.demon.nl   
      
   Python  wrote:   
      
   > Le 27/11/2025 à 22:44, Maciej Wo?niak a écrit :   
   > > On 11/27/2025 10:12 PM, Thomas 'PointedEars' Lahn wrote:   
   > >> Paul B. Andersen wrote:   
   > >>> Den 26.11.2025 12:52, skrev J. J. Lodder:   
   > >>>> Summary: The GPS sat clocks are steered such that they are synchronous   
   > >>>> with the GPS master clocks at USNOP.   
   > >>>> (applying the appropriate corrections, Doppler and relativity)   
   > >>>   
   > >>> There is no correction for the Doppler shift due to the velocity   
   > >>> of the SVs relative to the receiver.   
   > >>> The gravitational Doppler shift is included in the (1-4.4647e-10)   
   > >>> rate correction of the SV clock.   
   > >>   
   > >> Gravitational redshift is NOT a Doppler shift (it arises from spacetime   
   > >> curvature, not relative motion?), but my professor in General   
   > >> Relativity has confirmed to me that the interpretation of gravitational   
   > >> redshift as   
   > >   
   > >   
   > > But was Riemann claiming that Earth surface   
   > > is an obvious counterexample against Pythagorean   
   > > theorem [and the rest of Euclid's geometry]?   
   >   
   > I seriously doubt Riemann ever claimed anything of that kind :-)   
      
   Riemann had no doubt seen that the validity of the Pythagorean theorem   
   defines Euclidean geometry. (and vice versa)   
      
   And of course that in the internal geometry in a spherical surface   
   does not safisfy the Euclidean axiom.   
   This was hardly news of course,   
   the ancient Greeks already knew all about spherical trigonometry,   
   (derived from Euclidean geometry of course)   
      
   Jan   
      
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