Tag Archives: Hyperbolic Geometry

How to plot functions with LaTeX

Saddle surface

Following on a previous blog post on drawing fractals with LaTeX, today I am going to plot functions using LaTeX. As in the previous post, let’s start by preparing the LaTeX environment from scratch:

The pgfplots package for plotting functions and the standalone package for displaying the graph in a single document need to be installed manually as they are not currently present in the Ubuntu repositories:

To get started I am going to plot two simple functions which can be mathematically expressed as follows:

The first function is a linear function whose graph is a straight line. The second one is a quadratic function whose graph is a parabola. Here is the code to plot them with LaTeX:

To compile the tex file into pdf from the command line you can use the latexmk utility previously installed and open the generated file with your preferred PDF editor (I use evince here).

The plotted functions look like this (and like this in PDF):

Plotting linear and quadratic functionsThe next graph is obtained by joining a sequence of points whose coordinates on the x and y axis are clearly visible in the code (this example is adapted from the beautiful PGFPlots Gallery):

Again, I use latexmk to compile the code and evince to open the PDF.

The plotted function looks like this (and like this in PDF):

plot pointsFinally, I’m going to draw a saddle surface. This is an example of hyperbolic geometry, a non-Eucledian geometry where the postulate of parallel lines doesn’t hold. Popular examples of hyperbolic geometry are the Pringles crisps and print works by the Dutch artist M. C. Escher. So here is the LaTeX code to generate a saddle surface:

As usual, I compile it with latexmk and open it with evince.

And here is the beautiful saddle surface (and here is the associated PDF):

Saddle surface
Saddle surface


Mihalis Tsoukalos, LaTeX: Make text beautiful, Linux Format 201, Summer 2015