\documentclass[11pt]{article} % Simple LaTeX document by David J C MacKay % AIMS October 2006 % This article includes an equation, a figure, and % a bibliography. % See also {\tt{/home/mackay/tex/citedemo.tex}}. % % PACKAGES % \usepackage{graphicx} \usepackage{epsfig}% Another package for including postscript figures \usepackage{natbib}% To change the citation style, modify this line \usepackage{setspace} %% This command... %\setstretch{1.5} %% ... and this one make the document double-spaced %%% See http://www.image.ufl.edu/help/latex/spacing.shtml %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% END OF PACKAGE LIST % % PAGE SIZE % \textheight=10.5in \textwidth=6.7in \oddsidemargin=-0.245in \topmargin=-1.0in % % Pick a bibliography-style. I recommend abbrvnat. % The natbib package supports many styles. % Change this style to change the appearance of the bibliography. % %\bibliographystyle{unsrtnat} %\bibliographystyle{plainnat} \bibliographystyle{abbrvnat} % % YOUR DOCUMENT % \begin{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Title, Author, Date \title{How High can Animals Jump?} \author{David J. C. MacKay -- {\tt mackay@aims.ac.za} %%% You can add more address details here, starting each new line with \\ } \date{\today\ -- Draft 1.1} \maketitle %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End of Title \begin{abstract} I present an explanation for why all animals can jump the same height. \end{abstract} \section{Introduction} % The top speed of an animal runnning on the % flat varies with the size % of the animal. A lion runs faster than a mouse. But what about jumping? I once trapped a mouse behind the bin in my kitchen. I was amazed to see it jump to a height of four feet. With this olympic feat, the mouse got away. \section{Theory of jumping} \label{secTheory} An animal is mainly muscle. If we assume that all animals' muscles have the same physiology, we might guess that in a single big jump, each little mass $\delta m$ of muscle can liberate an energy proportional to $\delta m$: \begin{equation} \delta E = \lambda \, \delta m , \label{eqDeltaE} \end{equation} %% \, inserts a small space where $\lambda$ is the constant of proportionality. Thus the total kinetic energy of an animal with mass $m$, immediately after it jumps, is %\begin{equation} $E = \lambda m $. % \end{equation} Once the animal reaches the top of its trajectory, all this energy gets turned into potential energy: % \begin{equation} $E = m g h_{\max}$. % \end{equation} So the maximum height reached is \begin{equation} h_{\max} = \frac{ \lambda }{ g } , \label{HeightEquation} \end{equation} {\em independent of the animal's size, $m$}. For similar reasons, while animals have different speeds on the flat, the top speed of an animal running up a hill is the same for all animals. For my next trick, I will explain why all birds have the same flying range -- from seagulls to Boeing 747s. \begin{figure}[h]%% using [h] forces the figure to be 'HERE' \begin{center} \includegraphics[width=3cm]{/home/mackay/tex/figs/balance.eps} \end{center} \caption{This animal has one leg and two arms.} \label{figBalance} \end{figure} \section{Discussion} Figure \ref{figBalance} shows a picture of an animal juggling 4 balls. \citet{Shannon48} was an expert juggler. Good error-correcting codes exist \citep{Shannon48}. I can refer to equation (\ref{eqDeltaE}) or to section \ref{secTheory}. You can get more help on \LaTeX\ here: {\tt{http://www.aims.ac.za/resources/tutorials/latex-xfig/}} The source of this file is {\tt{/home/mackay/tex/LatexExample.tex}}. My {\tt{.bib}} file is {\tt{/home/mackay/bibs.bib}}. Feel free to use these files as templates. \bibliography{/home/mackay/bibs.bib}%%% you should put your own %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% bib file here. \end{document}