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M3P2
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c03a99b0
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c03a99b0
authored
May 27, 2021
by
Claude Meny
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Update textbook.fr.md
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12.temporary_ins/06.geometry-coordinates/40.n4/10.main/textbook.fr.md
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c03a99b0
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@@ -172,9 +172,9 @@ unité d'invariant.
!!! où l'invariant prend cette forme est dit cartésien.
!!! Il existe d'autres systèmes de coordonnées, non cartésiens, dans lequel cet invariant a une forme différente :
!!! \- en coordonnées cylindriques $`
(
\r
ho,
\v
arphi,z)
`$ l'invariant distance euclidienne s'écrit
$`
dl^2=
\r
ho^2+
\r
ho^2
\c
dot d
\v
arphi^2+dz^2
`$.
!!!
$`
dl^2=
\r
ho^2+
\r
ho^2
\c
dot d
\v
arphi^2+dz^2
`$.
!!! \- en coordonnées sphérique $`
(r,
\t
heta,
\v
arphi)
`$ l'invariant distance euclidienne s'écrit
$`
dl^2=r^2+r^2
\c
dot d
\t
heta^2+ r^2
\s
in^2
\t
heta
z^2
`
$.
!!! $`
dl^2=r^2+r^2
\c
dot d
\t
heta^2+ r^2
\s
in^2
\t
heta
z^2
`
$.
!!! Mais quelque-soit le système de coordonnée utilisé avec une même unité de mesure, l'invariant distance euclidienne
a toujours la même valeur.
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