Triangle instead of circle in degrees

Question

How does one turn the circular degree symbol \textdegree

°

into an equilateral triangle degree symbol?

I am just very curious about this, I only know how to type up basic mathematics.

Answer 1

You can simple use ^ to make a triangle appear as a superscript:

\documentclass{article}

\begin{document}
    $15^\triangle$
\end{document}

or even smaller but requiring another package:

\documentclass{article}

\usepackage{mathabx}

\begin{document}
    $15^\smalltriangleup$
\end{document}

Answer 2

I was interested in an alternative symbol for the hypothetical scenario where one full turn is defined to be something other than 360 units.

Besides using other fonts, you may also draw your own symbols and use them like chracters. The code below:

• uses tikz and one of its libraries shapes.geometric, which provides a star shape
• the star can have other than 5 points and can degrade into a pentagon with its default of 5 beams
• to simplify use I introduced a shortcut \turn
• inside it simply draws and rescales the star \tikz[scale=.5,transform shape]{\node[star,draw,star point height=7pt]{};}
• to highlight some typographical effects the document simply repeats some text for the star and the triangle

\documentclass[10pt,a4paper]{article}

% ~~~ cfor reating visuals ~~~~~~~~~
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}

% ~~~ shortcut ~~~~~~~~~~
\newcommand\turn[0]{\tikz[scale=.5,transform shape]{\node[star,draw,star point height=7pt]{};}}

% ~~~ document ~~~~~~~~~~~~~~~~
\begin{document}
    Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$. Some text using $15^{\turn}$.
    \bigskip
    
    Some text using $15^\triangle$. Some text using $15^\triangle$. Some text using $15^\triangle$. Some text using $15^\triangle$. Some text using $15^\triangle$. Some text using $15^\triangle$. Some text using $15^\triangle$. Some text using $15^\triangle$. Some text using $15^\triangle$. 
\end{document}