Indentation in proof environment within description environment

Question

I currently have

\documentclass[10pt]{article}
\usepackage[text={7.2in,9.6in}]{geometry}
\geometry{letterpaper}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}

\begin{document}
\begin{description}
\item[Problem 8~]
A woman starts at a point $P$.

\begin{proof}[Response]
The north pole is such a point. And there are others: 
Consider a point $a_1$ near the south pole such that 
the parallel passing through $a_1$ forms a 
circle $C_1$ with circumference exactly one mile.

If a point $a_2$ (or $a_3, a_4, \ldots$) is chosen 
near the south pole so that the parallel passing 
through it forms a circle $C_2$ ($C_3, C_4, \ldots$) 
with a circumference of exactly $\frac{1}{2}$ mile 
($\frac{1}{3}$ mile, $\frac{1}{4}$ mile, \ldots), 
then the point
\end{proof}
\end{description}

\begin{proof}[Response]
The north pole is such a point. And there are others: 
Consider a point $a_1$ near the south pole such that 
the parallel passing through $a_1$ forms a 
circle $C_1$ with circumference exactly one mile.

If a point $a_2$ (or $a_3, a_4, \ldots$) is chosen 
near the south pole so that the parallel passing 
through it forms a circle $C_2$ ($C_3, C_4, \ldots$) 
with a circumference of exactly $\frac{1}{2}$ mile 
($\frac{1}{3}$ mile, $\frac{1}{4}$ mile, \ldots), 
then the point
\end{proof}
\end{document}

which produces the following:

My goal is to have the second paragraph in the "response" in the proof environment within the description environment indented like it is outside of the description environment.

I imagine the problem may be in how I am using the geometry package, but I am unsure. Is there a way to have the second paragraph indented (and also no added white space) after a new line break in the proof environment within the description environment?

Answer 1

No, geometry has no role in this. The problem is that proof uses internally trivlist, which inherits some of its parameters from the enclosing description environment.

You can define your own environment that restores the relevant parameters.

\documentclass[10pt]{article}
\usepackage[text={7.2in,9.6in}]{geometry}
\geometry{letterpaper}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}

\newlength{\normalparindent}
\newlength{\normalparskip}
\AtBeginDocument{%
  \setlength{\normalparindent}{\parindent}%
  \setlength{\normalparskip}{\parskip}%
}

\newenvironment{response}
 {\proof[Response]%
  \setlength{\parskip}{\normalparskip}%
  \setlength{\parindent}{\normalparindent}}
 {\endproof}

\begin{document}
\begin{description}
\item[Problem 8~]
A woman starts at a point $P$.

\begin{response}
The north pole is such a point. And there are others: 
Consider a point $a_1$ near the south pole such that 
the parallel passing through $a_1$ forms a 
circle $C_1$ with circumference exactly one mile.

If a point $a_2$ (or $a_3, a_4, \ldots$) is chosen 
near the south pole so that the parallel passing 
through it forms a circle $C_2$ ($C_3, C_4, \ldots$) 
with a circumference of exactly $\frac{1}{2}$ mile 
($\frac{1}{3}$ mile, $\frac{1}{4}$ mile, \ldots), 
then the point
\end{response}
\end{description}

\begin{response}
The north pole is such a point. And there are others: 
Consider a point $a_1$ near the south pole such that 
the parallel passing through $a_1$ forms a 
circle $C_1$ with circumference exactly one mile.

If a point $a_2$ (or $a_3, a_4, \ldots$) is chosen 
near the south pole so that the parallel passing 
through it forms a circle $C_2$ ($C_3, C_4, \ldots$) 
with a circumference of exactly $\frac{1}{2}$ mile 
($\frac{1}{3}$ mile, $\frac{1}{4}$ mile, \ldots), 
then the point
\end{response}
\end{document}

Answer 2

Or, use the enumitem package:

\documentclass[10pt]{article}
\usepackage[text={7.2in,9.6in}]{geometry}
\geometry{letterpaper}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{enumitem}

\begin{document}
\begin{description}[listparindent=\parindent,parsep=0pt]
\item[Problem 8~]
A woman starts at a point $P$.

\begin{proof}[Response]
The north pole is such a point. And there are others: 
Consider a point $a_1$ near the south pole such that 
the parallel passing through $a_1$ forms a 
circle $C_1$ with circumference exactly one mile.

If a point $a_2$ (or $a_3, a_4, \ldots$) is chosen 
near the south pole so that the parallel passing 
through it forms a circle $C_2$ ($C_3, C_4, \ldots$) 
with a circumference of exactly $\frac{1}{2}$ mile 
($\frac{1}{3}$ mile, $\frac{1}{4}$ mile, \ldots), 
then the point\ldots

One additional paragraph.
\end{proof}
\end{description}

\begin{proof}[Response]
The north pole is such a point. And there are others: 
Consider a point $a_1$ near the south pole such that 
the parallel passing through $a_1$ forms a 
circle $C_1$ with circumference exactly one mile.

If a point $a_2$ (or $a_3, a_4, \ldots$) is chosen 
near the south pole so that the parallel passing 
through it forms a circle $C_2$ ($C_3, C_4, \ldots$) 
with a circumference of exactly $\frac{1}{2}$ mile 
($\frac{1}{3}$ mile, $\frac{1}{4}$ mile, \ldots), 
then the point
\end{proof}
\end{document}

For completeness’ sake, here is the output:

---

Addition

A better solution involves creating your custom “description-like” environment:

\documentclass[10pt]{article}
\usepackage[text={7.2in,9.6in}]{geometry}
\geometry{letterpaper}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{enumitem}

\newlist{DWRdescription}{description}{1} % <<< Increase last argument if you 
                                         %     need to nest "DWRdescription" 
                                         %     environments.
\setlist[DWRdescription]{listparindent=\parindent,parsep=0pt}



\begin{document}

\begin{DWRdescription}
    
\item[Problem 8~]
A woman starts at a point $P$.

\begin{proof}[Response]
The north pole is such a point. And there are others: 
Consider a point $a_1$ near the south pole such that 
the parallel passing through $a_1$ forms a 
circle $C_1$ with circumference exactly one mile.

If a point $a_2$ (or $a_3, a_4, \ldots$) is chosen 
near the south pole so that the parallel passing 
through it forms a circle $C_2$ ($C_3, C_4, \ldots$) 
with a circumference of exactly $\frac{1}{2}$ mile 
($\frac{1}{3}$ mile, $\frac{1}{4}$ mile, \ldots), 
then the point\ldots

One additional paragraph.
\end{proof}

\end{DWRdescription}

\begin{proof}[Response]
The north pole is such a point. And there are others: 
Consider a point $a_1$ near the south pole such that 
the parallel passing through $a_1$ forms a 
circle $C_1$ with circumference exactly one mile.

If a point $a_2$ (or $a_3, a_4, \ldots$) is chosen 
near the south pole so that the parallel passing 
through it forms a circle $C_2$ ($C_3, C_4, \ldots$) 
with a circumference of exactly $\frac{1}{2}$ mile 
($\frac{1}{3}$ mile, $\frac{1}{4}$ mile, \ldots), 
then the point
\end{proof}
\end{document}

The output should be exactly the same as before.