Want to combine LaTeX article class design with beamer convenience

Question

To make a presentation I've tried beamer in the past, but it did not turn out the way I wanted. I like the LaTeX layout so much that I would also like to use it for presentations. Currently with beamer I can not make a nice calm looking presentation as I can with a LaTeX article.

I have made my own simple LaTeX alternative to beamer. I rotate a page and fix the spacing and scale everything nicely. In my environment unfortunately I can't make use of the nice \pause command that beamer has. So I have to allow lots of double code. Also I have to end all slides with a lot of extra vertical whitespace, otherwise the current slide will not be vertically aligned the same as the previous slide.

Does anyone have suggestions on how to improve my LaTeX presentation environment (eg add a pause command) or can anyone make a beamer style with normal looking LaTeX sections (instead of using frametitle) and a real LaTeX feel to it?

A minimal working example of what I would like to achieve:

\documentclass[a4paper]{article}
\renewcommand\familydefault{\sfdefault}
\long\def\/*#1*/{}
\usepackage[english]{babel}
\usepackage{mathtools}
\usepackage[T1]{fontenc}
\usepackage{amsmath, amsthm, amsfonts, mathrsfs, amsfonts, amssymb}
\usepackage{adjustbox}

%------------------------------------------------------------------------------
% MACRO'S 
%------------------------------------------------------------------------------

\newcommand{\ds}{\displaystyle}

\pagenumbering{arabic}
%\pagenumbering{gobble}
\renewcommand*{\thepage}{\large{\arabic{page}}}

\usepackage{lscape} %write to page horizontally

\newcommand\horizontalpage[1]{
    \begin{landscape}
    \thispagestyle{empty}
        \begin{table}[htbp]
            \centering
            \adjustbox{width = 1.7\textwidth}{\begin{minipage}{\textwidth}
                #1 \ \vfill
            \end{minipage}}
                %\raisebox{-5cm}{\thepage} % uncomment to print page numbers
            \end{table}
        \global\pdfpageattr\expandafter{\the\pdfpageattr/Rotate 90} %when written horizontally, rotate back

    \end{landscape} 
}

\newcommand\myItemize[1]{
\begin{itemize}
  \setlength\itemsep{0em}
  #1
\end{itemize} 
}
\newcommand\myEnumerate[1]{
\begin{enumerate}
  \setlength\itemsep{0em}
  #1
\end{enumerate}
}


\begin{document}
\horizontalpage{
\title{Catalan Numbers}
\author{Max van Delft}
\maketitle
\thispagestyle{empty} %to remove the page number from the title page, see https://tex.stackexchange.com/questions/1736/removing-page-number-for-title-page
}

\horizontalpage{ 
\section{Introduction} 
\subsubsection*{Historic outline} 
Around 1750 Euler had found, but not proven, a recurrence relation for the enumeration of triangulations of a regular polygon. Euler discussed the problem with Segner, a mathematician from Hungary. The latter found a now well known recurrence relation. The Catalan number sequence was popularised in France around the 1840's. Then in 1838 the Belgian mathematician Catalan came across the sequence during his research of balanced parentheses, referring to them as Segner numbers. Later in the 20th century the numbers were named after Catalan. 
}

\horizontalpage{ 
\setcounter{section}{0}
\section{Introduction} 
Catalan numbers occur quite regularly in enumerative combinatorics. Objects the enumeration of which yield the Catalan numbers are called \textit{Catalan Objects}.
%
\subsubsection*{Examples}
\myItemize{
\item Triangulations of an $(n+2)$'gon 
\item Ordered multiplications of $(n+1)$ factors
\item $n$ Balanced parentheses
\item Dyck paths of length $2n$
\item Non-crossing partitions of $\{1,...,n\}$.
} \ \\ \\ \\ \\
}

\horizontalpage{ 
\setcounter{section}{0}
\section{Introduction} 
Catalan numbers occur quite regularly in enumerative combinatorics. Objects the enumeration of which yield the Catalan numbers are called \textit{Catalan Objects}.
%
\subsubsection*{Examples}
\myItemize{
\item Triangulations of an $(n+2)$'gon 
\item Ordered multiplications of $(n+1)$ factors
\item $n$ Balanced parentheses
\item Dyck paths of length $2n$
\item Non-crossing partitions of $\{1,...,n\}$.
} 
\subsubsection*{Bijections}
We will present bijections between the Catalan objects listed above. \\ \\ \\ \\
}

\end{document}

Answer 1

The following beamer based MWE looks at least somehow similar to your presentation. Probably you can use it as a place to start from:

beamer based version _________________________article based version

\documentclass[t]{beamer}
\beamertemplatenavigationsymbolsempty
\setbeamertemplate{itemize items}[circle] 
\setbeamercolor{structure}{fg=black}

\setbeamerfont{frametitle}{series=\bfseries,parent=structure}

\usepackage{ragged2e}
\usepackage{etoolbox}
\apptocmd{\frame}{}{\justifying}{}
\begin{document}

\begin{frame}
\title{Catalan Numbers}
\author{Max van Delft}
\maketitle
\end{frame}


\section{Introduction} 
\begin{frame}{\thesection. \secname}
\textbf{Historic outline}

Around 1750 Euler had found, but not proven, a recurrence relation for the enumeration of triangulations of a regular polygon. Euler discussed the problem with Segner, a mathematician from Hungary. The latter found a now well known recurrence relation. The Catalan number sequence was popularised in France around the 1840's. Then in 1838 the Belgian mathematician Catalan came across the sequence during his research of balanced parentheses, referring to them as Segner numbers \cite{Pak2014}. Later in the 20th century the numbers were named after Catalan. 
\end{frame}

\begin{frame}{\thesection. \secname}


Catalan numbers occur quite regularly in enumerative combinatorics. Objects the enumeration of which yield the Catalan numbers are called \textit{Catalan Objects}.

\medskip\textbf{Examples}
\begin{itemize}
\item Triangulations of an $(n+2)$'gon 
\item Ordered multiplications of $(n+1)$ factors
\item $n$ Balanced parentheses
\item Dyck paths of length $2n$
\item Non-crossing partitions of $\{1,...,n\}$.
\end{itemize}

\pause

\medskip\textbf{Bijections}

We will present bijections between the Catalan objects listed above.
\end{frame}


\end{document}

Answer 2

Just for variety.

Note that TeXpower does not automatically pause between items. Wasn't sure if you wanted that or not.

\documentclass{article}
\usepackage{xcolor}
\usepackage[screen,nopanel]{pdfscreen}
\usepackage[display]{texpower}
\margins{0.25in}{0.25in}{0.25in}{0.25in}
\screensize{4.5in}{6in}
\backgroundcolor{lightgray}

\renewcommand\familydefault{\sfdefault}
\long\def\/*#1*/{}
\usepackage[english]{babel}
\usepackage{mathtools}
%\usepackage[T1]{fontenc}
%\usepackage{amsmath, amsthm, amsfonts, mathrsfs, amssymb}
%\usepackage{adjustbox}

%------------------------------------------------------------------------------
% MACRO'S 
%------------------------------------------------------------------------------

\newcommand{\ds}{\displaystyle}

\pagenumbering{arabic}
%\pagenumbering{gobble}
\renewcommand*{\thepage}{\large{\arabic{page}}}

\newcommand\myItemize[1]{
\begin{itemize}
  \setlength\itemsep{0em}
  #1
\end{itemize} 
}
\newcommand\myEnumerate[1]{
\begin{enumerate}
  \setlength\itemsep{0em}
  #1
\end{enumerate}
}

\title{Catalan Numbers}
\author{Max van Delft}

\begin{document}
\begin{slide}
\vbox{\maketitle}
\end{slide}
\pause

\section{Introduction} 
\stepwise*{% start with step 1
\steponce{%
\subsubsection*{Historic outline} 
Around 1750 Euler had found, but not proven, a recurrence relation for the enumeration of triangulations of a regular polygon. Euler discussed the problem with Segner, a mathematician from Hungary. The latter found a now well known recurrence relation. The Catalan number sequence was popularised in France around the 1840's. Then in 1838 the Belgian mathematician Catalan came across the sequence during his research of balanced parentheses, referring to them as Segner numbers \cite{Pak2014}. Later in the 20th century the numbers were named after Catalan.}

\step{%
Catalan numbers occur quite regularly in enumerative combinatorics. Objects the enumeration of which yield the Catalan numbers are called \textit{Catalan Objects}.}

\step{%
\subsubsection*{Examples}
\myItemize{%
\item Triangulations of an $(n+2)$'gon 
\item Ordered multiplications of $(n+1)$ factors
\item $n$ Balanced parentheses
\item Dyck paths of length $2n$
\item Non-crossing partitions of $\{1,...,n\}$.
}}

\step{%
\subsubsection*{Bijections}
We will present bijections between the Catalan objects listed above.
}}

\end{document}