March, 2012: Möbius Transformations in a Tangle
We saw in a previous post a kind of transformation of complex values, a Möbius transformation. It turns out that we can decompose any Möbius transformation into a series of four separate transformations – a translation, an inversion, a dilation/rotation, and a final transformation. From a UX perspective, we saw that using input fields and a button to modify the transformation was not slick. Today we’re going to make things more slick.
March, 2012: NAntScript, now with added functions
When we’re doing C# work, we’re fairly big fans of NAnt, as it’s a very good build system for .Net. However, it’s got a few small flaws, the main one of which is that you often end up repeating yourself a fair few times, and applying any sort of DRY thinking in it is quite hard.
Enter NAntScript. Originally from some folks elsewhere, but languishing and somewhat abandoned and in need of some work. The core idea being that you can write new tasks for NAnt using existing tasks (it is in fact also possible to write new NAnt tasks using C# or various other languages, but that’s a pretty messy way to work) (more…)
March, 2012: D3 glasses and the Complex Plane
One of the best ways to develop intuition in mathematics is to look at pictures. We often use graphs – visual representations of functions – showing the relationship between the domain of a function and the range of a function. With real-valued functions of one variable this is easy: the graph is nice and flat. What about complex-valued functions? What kind of pictures would help?
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