Last updated 17jan15.## Axiomatic Sytems for Geometry

\textit{ $\C$ 2010, Prof. George K. Francis, Mathematics Department, University of Illinois}

\begin{document} \section{Introduction} This lesson introduces you to the Axiomatic Method. Among other reasons, the logical rigor involved in this approach to geometry, and human knowledge in general, is why it has been taught to school children for 2.3 millenia. Indeed, Abraham Lincoln studied Euclid by firelight in that log cabin in Kentucky. Some students appreciate a concise overview of the material to be covered for a large chunk of the course. Other students prefer to have a concise summary of what they have learned. Either way, the linked document serves both purposes. You are \textbf{NOT} expected to understand every part of the story the first or even the second time you read it. But by the time you review the material learned in preparation for an test, you will appreciate it better. \section{Mathematical Writing} For this course you will need to master a beginner's portion of the universal mathematical typesetting language, LaTeX (pronounced ``lah-tec'' in American English. Be careful not confuse TeX with `text'. So you may want to go a bit further and consider writing an essay in LaTeX. The lessons on this website which are written in MathML are in the HTML format. That means, if you want to see how a mathematical formula is coded, you can just look at the source of the web page. Consult the Advice pages for more detail. But to see the code for a page typeset in the PDF format you cannot do this as easily. So here is postulates.tex , which is the source code to the document. \section{Illustrations } Whenever you use an image obtained from anyone other than your own work, you are expected to give credit to its author. You should never just copy an image from the web and use it in your own work. I found the image at the top on the webpages of a prestigious high school, without credits. I was suspicious, because the image itself has a signature. I traced it down to it's artist in Germany. I then edited the url of the author right into the image, using Paint (or Paintbrush on a mac), as described in Advice. This way, if anyone steals my copy of this image, it will carry the reference with it. I recomment to adopt this in your college work as well.