[gnuastro-commits] master f257888: Book: typo fixed in section Distance on a 2D curved space

[Mohammad Akhlaghi]

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.