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…

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…

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.…