How to make a QED symbol based on Unicode's Lower Right Triangle?

Question

I want to make a symbol which looks like the unicode lower right triangle U+25FF but with the same size and line thickness as the \qed symbol.

If I resized the unicode symbol with \resizebox the line thickness wouldn't be the same, so I need a new symbol. I don't know how to do it.

Answer 1

In amsthm.sty we find

% amsthm.sty, line 422:
\newcommand{\openbox}{\leavevmode
  \hbox to.77778em{%
  \hfil\vrule
  \vbox to.675em{\hrule width.6em\vfil\hrule}%
  \vrule\hfil}}
% amsthm.sty, line 430:
\providecommand{\qedsymbol}{\openbox}

so we want to build a triangle based on those dimensions.

\documentclass{article}
\usepackage{amsmath,amsthm,pict2e}

\usepackage{color} % for the comparison

\newcommand{\opentriangle}{%
  \raisebox{0.2pt}{\makebox[0.77778em]{%
    \setlength{\unitlength}{0.6em}%
    \linethickness{0.4pt}%
    \begin{picture}(1,1)
    \polygon(0,0)(1,0)(1,1)
    \end{picture}%
  }}%
}
\renewcommand{\qedsymbol}{\opentriangle}

\begin{document}

First a comparison: 
\openbox\opentriangle\quad
\makebox[0pt][l]{\openbox}\textcolor{red}{\opentriangle}\quad
\makebox[0pt][l]{\opentriangle}\textcolor{red}{\openbox}

\begin{proof}
The two symbols are not exactly one half of the other, 
but the difference can't be noticed if they aren't
superimposed on each other.
\end{proof}

\end{document}

Depending on the main document font, you might prefer round joins:

Just change the code into

\newcommand{\opentriangle}{%
  \raisebox{0.2pt}{\makebox[0.77778em]{%
    \setlength{\unitlength}{0.6em}%
    \linethickness{0.4pt}\roundjoin
    \begin{picture}(1,1)
    \polygon(0,0)(1,0)(1,1)
    \end{picture}%
  }}%
}

Answer 2

If you're free to use the stix math font package, you could make use of its \lrtriangle -- shorthand for "lower right triangle, I suppose -- macro. The package's \square and \lrtriangle macros produce symbols that have the same size and line thickness.

To make \lrtriangle the QED symbol, one could load the amsthm or ntheorem package and execute \renewcommand\qedsymbol{\lrtriangle}.

\documentclass{article}
\usepackage{stix,color}
\begin{document}
$\square \lrtriangle$

% same horizontal and vertical dim., same line thickness:
$\square\color{red}\kern-9.1pt\lrtriangle$
\end{document}