A non-integer representation uses non-integer numbers as the radix, or bases, of a positional numbering system. For a non-integer radix β > 1, the value of
:x=d_n\dots d_2d_1d_0.d_{-1}d_{-2}\dots d_{-m}
is
:x=\beta^nd_n + \cdots + \beta^2d_2 + \beta d_1 + d_0 + \beta^{-1}d_{-1} + \beta^{-2}d_{-2} + \cdots + \beta^{-m}d_{-m}.
The numbers di are non-negative integers less than β. This is also known as a β-expansion, a notion introduced by and first studied in detail by . Every real number has at least one (possibly infinite) β-expansion.
There are applications of β-expansions in coding th...
Taking the posted example, adding the following check seems to work
\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,shapes}
\makeatletter
\AtEndDocument{%
\let\oldpgfsyspdfmark\pgfsyspdfmark
\def\pgfsyspdfmark#1#2#3{%
\expandafter\let\expandafter\tmp\csnam...
