Resize (shrink) the entire document after resizing (expanding) it once

Question

Problem

Context

I was trying to make a multi-column document, but found that the content wasn't being displayed properly as there was a display equation spilling over into the other column. My first solution (which worked) was to use the geometry package to set the paperwidth and paperheight to be the values for A4-paper * 1.5 (315mm and 445.5mm, respectively). This worked perfectly and I am happy with the layout of the document, but I would like the exported PDF to still be A4 sized (sort of like what Adobe Acrobat's pre-flight fixups do).

This is where I am hitting a dead end. I've tried googling this, but to no avail. Some suggest using the pdfpages package to load it in as a separate PDF file and just scale it down from there, but I would like to keep this in a single TeX file, if possible.

The actual problem

How can I shrink the entire document, which has been enlarged to 1.5x A4-paper, back down to A4-paper size, but keeping the layout and formatting of the enlarged (1.5xA4-paper size) document??

Minimum Reproducible Example

\documentclass[12pt,titlepage]{article}
\usepackage[margin=2cm, paperwidth=315mm, paperheight=445.5mm]{geometry}
\usepackage{multicol}
\usepackage{xspace}
\usepackage{microtype}
\usepackage{lipsum}
\usepackage{siunitx}
\title{MRE - Resizing entire document}
\author{BrightBulb123}
\begin{document}
\maketitle

\begin{multicols}{2}

    \section{Introduction}

    \lipsum[1-2]

    $$\frac{F_{\text{g}_{\text{Earth-Mars}}}}{F_{\text{g}_{\text{Earth-Sun}}}}\times100=\frac{\num{3.0e+16}}{\num{3.4e+22}}\times100\approx\num{8.8e-05}\%=0.000088\%$$  % troublesome equation

    \lipsum[2-5]

\end{multicols}


\end{document}

Screenshots

What I had before

What I have now (enlarged page size)

Essentially, what I want is to just shrink down that second image to A4-paper size.

---

Edits

Edit 1

I want to clarify that it doesn't matter if it looks ugly or illegible at first glance. This is just a personal project of mine, not something that I will be showcasing professionally.

I just want to see how to do it from within the document's code itself, without using any external tools.

Edit 2

This post is similar to what I want to do (I'm just doing it backwards (shrinking instead of expanding)).

Answer 1

I assume, that your page margins are 2cm. In this case, when for siunitx is set tight-spacing, than equation not protrude right column border. But you may find @ MS-SPO comment useful. Using for example align* split equation into two lines and by this make it much narrower.

There is one more possibilities. Using nccmath package (which is extension of amsmath, so it also load it) and its macro \medmath make equation smaller. See if this an acceptable option for you.

\documentclass[12pt,titlepage]{article}
\usepackage[margin=2cm]{geometry}
%--------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%
\usepackage{lipsum}                             % for dummy text
%---------------------------------------------------------------%
\usepackage{lipsum}
\usepackage{multicol}
\usepackage{xspace}
\usepackage{microtype}
\usepackage{siunitx}
\usepackage{nccmath}
\title{MRE - Resizing entire document}
\author{BrightBulb123}
\begin{document}
\maketitle
\begin{multicols}{2}
\section{Introduction}
\lipsum[1-5]
[
\sisetup{tight-spacing}
\frac{F_{\text{g}{\text{Earth-Mars}}}}
     {F{\text{g}{\text{Earth-Sun}}}}\times100
        = \frac{\num{3.0e+16}}{\num{3.4e+22}}\times100
        \approx\qty{8.8e-05}{%}
]  % troublesome equation
However, above equation you can write as
\begin{align*}
\frac{F{\text{g}{\text{Earth-Mars}}}}
     {F{\text{g}_{\text{Earth-Sun}}}}\times100
    & = \frac{\num{3.0e+16}}{\num{3.4e+22}}\times100 \ 
    & \approx\qty{8.8e-05}{%}

\end{align*}
Another possibilities is use \verb+\medmath', which make equation about 20% smaller:
[\medmath{
\frac{F_{\text{g}{\text{Earth-Mars}}}}
     {F{\text{g}_{\text{Earth-Sun}}}}\times100
    = \frac{\num{3.0e+16}}{\num{3.4e+22}}\times100 \
\approx\qty{8.8e-05}{%}
}]
\lipsum[5-11]
\end{multicols}
\end{document}

(red lines indicate text box borders).

Answer 2

Something you could always do, but what I don't recommend, is using local overwrites, localized by a pair of { }. Here I used \tiny, because \small wasn't small enough.

As you can see, it has some side effects, because LaTeX tries to fill the page as good as possible.

Some thoughts and suggestions

However, from a writing philosophy perspective it reminds me more of a WORD-approach. Why not adopting the style, which the academic community uses, e.g. through the article-class?

Why don't you introduce and use here abbreviations for the long force-indices? The naming here is a big part of your problem. Also the "100", i.e. percentage calculations. Either your audience is familiar with that, or you can introduce it somewhere, e.g. in an appendix?

For references, do you know the wikibook on LaTeX, e.g. the section about advanced maths?

Google can be your friend. E.g. entering as search term ctan resizing points to package resizegather. Follow the ctan-links about the topic and see also categories.

This site is your friend. E.g. looking to the right column at Related there's this link, which may or may not help you with package geometry and resizing.

However, still wondering what kind of visual concept your writing will present to me, the reader?

(Desert of blackness - with poor eye navigation)

Code

% https://tex.stackexchange.com/questions/684318/resize-shrink-the-entire-document-after-resizing-expanding-it-once
%\documentclass[12pt,titlepage]{article}
%
%\usepackage[margin=2cm, paperwidth=315mm, paperheight=445.5mm]{geometry}
\documentclass[12pt,a4paper]{article}
\usepackage[margin=2cm]{geometry}
\usepackage{multicol}
%\usepackage{xspace}
%\usepackage{microtype}
\usepackage{lipsum}
\usepackage{siunitx}
\title{MRE - Resizing entire document}
\author{BrightBulb123}
\begin{document}
\maketitle

\begin{multicols}{2}

    \section{Introduction}

    \lipsum[1-4]

{% scoping / local change
\tiny
        [\frac{F_{\text{g}{\text{Earth-Mars}}}}{F{\text{g}_{\text{Earth-Sun}}}}\times100=\frac{\num{3.0e+16}}{\num{3.4e+22}}\times100\approx\num{8.8e-05}%]  % troublesome equation
}
        \lipsum[5-11]
\end{multicols}


\end{document}