# Testing LaTEX and Quartic Roots

This post is simply a test of the LaTEX plugin that I supposedly have installed on this blog.  I haven’t used it in conjunction with Windows Live Writer Beta, my preferred blog writing software.

Feel free to sing along to the tune of “Pop Goes the Weasel” as you read the quadratic formula below:

$x = \displaystyle \frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Speaking of which, I introduced my algebra students to the fact that there exist some rather lengthy formulas for solving cubic and quartic equations. In fact, the four roots of the quartic equation,

$x^4 + ax^3 + bx^2 + cx + d= 0$

can be found in four individual equations over at Planet Math. I dare you to make your algebra students memorize those for the next exam.

# LaTEX Collaboration site

Move over Google Docs, there’s a new option for LaTEXies like myself. I still need to play with it a bit, but MonkeyTex gives the option of editing, storing, sharing and collaborating LaTEX documents. It has bibtex support as well as style sheets.

I’d like to use it as a way to train my students in typesetting their mathematics papers with LaTEX.

# Online LaTEX Renderer

LaTeX Equation Editor

This little tool could come in real handy. I chose to use WordPress as my blog engine so that I could make use of the LatexRender plugin, but there have been occasions where I’d have liked an additional tool like this. Seems to work quite well.

(And for those of you that aren’t aware, LaTEX is the tool most mathematicians make use of for typesetting)

# Using LaTEX with Geometers Sketchpad

(By the way, the word LaTEX is pronounced as lay-tech or L-A-tech, and it is a typesetting language.)

I never have found a “great” tool for creating ideal graphics for my exams and worksheets for use in the classes that I teach. Ideally, there would be a program that would allow me to draw basic geometric shapes like triangles, quadrilaterals, regular and non-regular polygons, circles, ellipses, parabolas, hyperboles, general functions, three dimensional shapes and surfaces, etc. In most cases, a simple GUI would be preferred where I am able to “point-and-click” to create most of my images. Obviously in more intricate drawings I’d need an interface for graphing functions. Afterward, I’d like to be able to export the drawing into any format such as a png, jpeg, gif, tiff, wmf, emf, ps, or eps. I have always been able to create what I want by combining my skills from MS Paint, Maple, Matlab, Photoshop (which I no longer have access to), Macromedia Firefox, Paint Shop Pro (which I no longer have access to), MS Work, MS Publisher, Excel, or OpenGL in C++. I used some of the Department’s budget to buy Geometer’s Sketchpad a few years ago, but I never really learned to use it. Today, I decided to become at least a little more familiar with it and use it to create some simple drawings. I then wanted to import my graphics into a LaTEX document.

Below are the two procedures I used, since GSP does not allow an export directly to any format that I can use in LaTEX or pdfLaTEX.

1. Draw the image in Geometer’s Sketchpad. There’s a bit of a learning curve in this step but I am getting the gist of it.
Option I
2. Save the GSP object as a wmf (windows metafile)
3. Use GIMP (an open source, rough equivalent of Photoshop) and open the wmf file then save it as a jpeg image. It helped to “clean up” the graphic to create the wmf file as a large image (1000 x 1000 pixels) then resize to the smaller desired size (using cubic filter for resizing).
Option II
2. Do a screen capture in GSP (using ctrl-alt-PrintScreen to copy the active window to clipboard.
3. Open a new image in GIMP (big enough to contain the active window. I know that my screen resolution is no more than 1400×1050, so I use that.). Then paste.
4. Crop the portion of the this window containing my desired image.
5. Save this as a jpeg.

Use

\includegraphics[width=##in]{image/…}

to insert the image in the LaTEX file. Note that you must have \usepackage{graphicx} in the preamble of the LaTEX file.