Symbolic Computational Geometry in Python: Heron's Formula

Floating point numbers suck. Sometimes they're the best we've got, but they still suck. Floating point numbers are to math as Physics 101 lab measurements are to the laws of physics: you get basically what you expect, but with a margin of error tacked on. Sometimes that's okay. Sometimes it's not. But what choice do we have? I'm so glad you asked, because it turns out we have plenty.

But before we get into that, let's convince ourselves that we have a problem to solve. Luckily, this is really easy. Suppose we want to find out, for some terribly important reason, the area of the triangle with vertices at (3,4), (7,10), and (11, 161). We don't get pen and paper -- in fact, the only tool at our disposal is a Python shell. If we know some geometry, then our naive approach might go something like this:

Cheat Sheet: Windowing in Screen & Vim

As a lazy computer science student, I find myself working on programs over SSH a lot. This tends to pose some challenges. Unless you want to mess around with -X and -Y flags, all you get is one terminal to do all your work in. Having to work in this environment has taught me one lesson: When all you have is a terminal, everything looks like a window manager. Or something. Anyway. There are lots of ways to split up a terminal session, and this post covers some common commands involved.

Cracking General Substitution Ciphers

As some of you have requested, today we'll be talking about paper-and-pencil cryptography and how we can use computers to poke it full of holes!

We're going to start with some background on basic (pre-digital) cryptography. Then, we're going to describe the specific cipher we're attacking here, along with some standard paper-and-pencil approaches to cracking it. Thirdly, we'll discuss one algorithmic approach powered by a dictionary file. Then, we'll look at some Python scripts implementing the discussed ideas. Two different scripts will be provided: A bare-bones one written to be simple to understand, and a batteries-included fancy one which elegantly implements the main logic using coroutines.

By the end of this post, we'll know what this script is doing and why it works.