# Making inscribed and circumscribed polygons

I’m trying to create a graphic of two n-sided polygons bounding a circle in Beamer. I’ve gone to other questions here on TeX, but none of them really have what I need. I’m looking for something similar to the answer given here: https://tex.stackexchange.com/a/152250/122640, but with polygons on the outside and in the context of Beamer.

\documentclass{beamer}

\usetheme{Warsaw}

\title{Archimedes's Approximation of Pi}
\author{Daniel Rui}

\begin{document}

\begin{frame}
\frametitle{Approximation}
\begin{columns}
\column{0.6\textwidth}
Archimedes began by inscribing a hexagon inside a circle and finding its perimeter.
\column{0.4\textwidth}
\begin{center}
PICTURE HERE
\end{center}

\end{columns}
\end{frame}

\end{document}


Colors to distinguish the polygons would be appreciated. Thanks for your help!

• On the outside of what? Have you actually tried anything? Your text suggests you want them on the inside of something, but the question wants them outside of something (different?). I don't see why Beamer should make a difference. Did you run into problems with the solutions in Beamer? – cfr Jul 15 '18 at 23:26
• So I am thinking of say one hexagon around a circle and a smaller hexagon inside a circle. I tried manipulating the code given in the answer from the other post, but I don’t really understand how to get from their code to my result. – D.R Jul 15 '18 at 23:34
• this is given in the pgf/tikz manual regular polygon shape – percusse Jul 15 '18 at 23:50

There's no problem doing it in Beamer. But I don't really understand the problem as the answers to the other question seem to provide what you need.

Why not just something like this (but in Beamer, obviously)?

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\begin{document}

\tikz[ultra thin]{
\draw [magenta] (0,0) circle ({10pt+.5*\pgflinewidth});
\foreach \i [evaluate=\i as \j using {(100*(\i-6))/12}] in {6,...,18}
\node [regular polygon, draw=blue!\j!green, minimum size=20pt, regular polygon sides=\i] {};
}

\end{document}


• What about creating polygons circumscribing (outside) the circle? – D.R Jul 16 '18 at 19:56