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Do the catenary and a parabola that approximates the catenary, have the same minimum (maximum sag)?

IF plotted, it looks to me they do, and that they only difer somewhere on the "slope". (sorry for maybe not using the correct mathematical terms, my maths is really rusty after some years)

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    $\begingroup$ What parabola that approximates the catenary? Isn't unique. $\endgroup$ – Martín-Blas Pérez Pinilla Aug 25 '14 at 8:59
  • $\begingroup$ The one that is calculated as a second diff of the catenary equation and linearized (hope this makes sense. In my area, catenary is often simplified into a parabola like this) $\endgroup$ – U2ros Aug 25 '14 at 9:17
  • $\begingroup$ No.. ignore that... i mixed something up. Its the parabola thats derived as a series from the equation of catenary... but i can calculate that myself. Bah.. $\endgroup$ – U2ros Aug 25 '14 at 9:51

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