[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
[gnuastro-commits] master 8d977a9 2/3: Avoid centering warning by Texinf
From: |
Mohammad Akhlaghi |
Subject: |
[gnuastro-commits] master 8d977a9 2/3: Avoid centering warning by Texinfo |
Date: |
Mon, 23 Oct 2017 09:14:53 -0400 (EDT) |
branch: master
commit 8d977a9b66f07a1b3a2fc70f7a6ec877afcaaa86
Author: Mohammad Akhlaghi <address@hidden>
Commit: Mohammad Akhlaghi <address@hidden>
Avoid centering warning by Texinfo
In the "Extending distance concepts to 3D", there were multiple instances
of address@hidden' in the middle of a paragraph. This caused a warning by
Texinfo on the fact that `center' must be at the start of the line. To
correct it, all address@hidden's in this section now have their own
paragraph
(one empty line before and after them).
---
doc/gnuastro.texi | 30 ++++++++++++++++++++----------
1 file changed, 20 insertions(+), 10 deletions(-)
diff --git a/doc/gnuastro.texi b/doc/gnuastro.texi
index 3ea5c93..a611b64 100644
--- a/doc/gnuastro.texi
+++ b/doc/gnuastro.texi
@@ -16353,16 +16353,26 @@ coordinates instead of polar coordinates.
@mymath{\theta} is shown in
(the center of the sphere) and the point @mymath{O} is tangent to a
4D-sphere. In our 3D space, a generic infinitesimal displacement will
correspond to the following distance in spherical coordinates:
address@hidden(d\theta^2+\sin^2{\theta}d\phi^2).}Like
-the 2D creature before, we now have to assume an abstract dimension which
-we cannot visualize easily. Let's call the fourth dimension @mymath{w},
-then the general change in coordinates in the @emph{full} four dimensional
-space will be:
address@hidden(d\theta^2+\sin^2{\theta}d\phi^2)+dw^2.}But we can
-only work on a 3D curved space, so following exactly the same steps and
-conventions as our 2D friend, we arrive at: @dispmath{ds_s^2={dr^2\over
-1-Kr^2}+r^2(d\theta^2+\sin^2{\theta}d\phi^2).}In a non-static universe
-(with a scale factor a(t), the distance can be written as:
+
address@hidden(d\theta^2+\sin^2{\theta}d\phi^2).}
+
+Like the 2D creature before, we now have to assume an abstract dimension
+which we cannot visualize easily. Let's call the fourth dimension
address@hidden, then the general change in coordinates in the @emph{full} four
+dimensional space will be:
+
address@hidden(d\theta^2+\sin^2{\theta}d\phi^2)+dw^2.}
+
address@hidden
+But we can only work on a 3D curved space, so following exactly the same
+steps and conventions as our 2D friend, we arrive at:
+
address@hidden 1-Kr^2}+r^2(d\theta^2+\sin^2{\theta}d\phi^2).}
+
address@hidden
+In a non-static universe (with a scale factor a(t)), the distance can be
+written as:
+
@dispmath{ds^2=c^2dt^2-a^2(t)[d\chi^2+r^2(d\theta^2+\sin^2{\theta}d\phi^2)].}