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[gnuastro-commits] master f257888: Book: typo fixed in section Distance
From: |
Mohammad Akhlaghi |
Subject: |
[gnuastro-commits] master f257888: Book: typo fixed in section Distance on a 2D curved space |
Date: |
Sun, 5 Dec 2021 11:13:17 -0500 (EST) |
branch: master
commit f2578887e8f6ec4fe491134f6dc1057bc80af094
Author: Mohammad Akhlaghi <mohammad@akhlaghi.org>
Commit: Mohammad Akhlaghi <mohammad@akhlaghi.org>
Book: typo fixed in section Distance on a 2D curved space
Until now, while deriving the change in distance on a flat 2D space, we had
forgot to add the power-of-two on the left-side of the equal sign!
With this commit, the power-of-two has been added, and a minor edit has
also been made in the paragraph above to be more clear.
This typo was found by Zohreh Ghaffari.
---
doc/gnuastro.texi | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/doc/gnuastro.texi b/doc/gnuastro.texi
index b546de7..54ad8d1 100644
--- a/doc/gnuastro.texi
+++ b/doc/gnuastro.texi
@@ -21809,10 +21809,10 @@ In @ref{flatplane} the infinitesimal changes for each
polar coordinate are plott
plane.}
@end float
-Assuming an object is placed at a certain position, which can be parameterized
as @mymath{(x,y)}, or @mymath{(r,\phi)}, a general infinitesimal change in its
position will place it in the coordinates @mymath{(x+dx,y+dy)} and
@mymath{(r+dr,\phi+d\phi)}.
+Assuming an object is placed at a certain position, which can be parameterized
as @mymath{(x,y)}, or @mymath{(r,\phi)}, a general infinitesimal change in its
position will place it in the coordinates @mymath{(x+dx,y+dy)}, or
@mymath{(r+dr,\phi+d\phi)}.
The distance (on the flat 2D surface) that is covered by this infinitesimal
change in the static universe (@mymath{ds_s}, the subscript signifies the
static nature of this universe) can be written as:
-@dispmath{ds_s=dx^2+dy^2=dr^2+r^2d\phi^2}
+@dispmath{ds_s^2=dx^2+dy^2=dr^2+r^2d\phi^2}
The main question is this: how can the 2D creature incorporate the (possible)
curvature in its universe when it's calculating distances? The universe that it
lives in might equally be a curved surface like @ref{sphereandplane}.
The answer to this question but for a 3D being (us) is the whole purpose to
this discussion.
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