Talk:PlanetPhysics/Catacaustic
Original TeX Content from PlanetPhysics Archive[edit source]
%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: catacaustic %%% Primary Category Code: 42.15.-i %%% Filename: Catacaustic.tex %%% Version: 1 %%% Owner: pahio %%% Author(s): pahio %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}
\setlength{\topmargin}{0.00in} \setlength{\headsep}{0.00in} \setlength{\headheight}{0.00in} \setlength{\evensidemargin}{0.00in} \setlength{\oddsidemargin}{0.00in} \setlength{\textwidth}{6.5in} \setlength{\textheight}{9.00in} \setlength{\voffset}{0.00in} \setlength{\hoffset}{0.00in} \setlength{\marginparwidth}{0.00in} \setlength{\marginparsep}{0.00in} \setlength{\parindent}{0.00in} \setlength{\parskip}{0.15in}
\usepackage{html}
% this is the default PlanetPhysics preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners.
% almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts}
% used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
\begin{document}
Given a plane curve $\gamma$, its \emph{catacaustic} (Greek $\varkappa\alpha\tau\acute{\alpha}\, \varkappa\alpha\upsilon\sigma\tau\iota\varkappa \acute{o}\varsigma$ `burning along') is the envelope of a family of light rays reflected from $\gamma$ after having emanated from a fixed point (which may be infinitely far, in which case the rays are initially parallel).
For example, the catacaustic of a logarithmic spiral reflecting the rays emanating from the origin is a congruent spiral.\; The catacaustic of the exponential curve \,$y = e^x$\, reflecting the vertical rays \,$x = t$\, is the \htmladdnormallink{catenary}{http://planetphysics.us/encyclopedia/Catenary.html} \,$y = \cosh(x\!+\!1)$.
\end{document}