This project is the creation of David Halpern, Kaushik Harith, Adam Shelby, and Brad Guesman, for the Brown University math course Math 1540: Topics in Abstract Algebra. It visualizes the construction process of so called Geometrically Constructible Numbers.
If you're already familiar with the branch of algebra known as Galois theory (or are a geometry enthusiast), this project probably requires no further explanation. If you're not though, don't worry! Here's a little bit of background.
A question of interest to the geometers of classical times was "what numbers can you construct with a compass and a straight edge"? In other words, starting with the points (0, 0) and (1, 0) in the plane and allowing yourself to only draw a finite number of lines between two points and circles with center at one point and intersecting another, what points in the plane can you get to?
This may seem like a trivial question, but it turns out that it is not so easy to answer. In fact, it wasn't shown until 1796 that the regular 17-gon was constructible (by Gauss, when he was 18, naturally). To provide a true criterion for constructibility, one has to draw a connection between the idea of "geometrically constructible" and "algebraically constructible".
We've already mentioned what it means to be geometrically constructible. An algebraically constructible number is one which can be constructed from performing field operations (addition, multiplication, subtraction, division) and a finite number of square roots with rational numbers. If you know some algebra, you'll recognize this as performing successive field extensions to the rationals.
We won't go into the proof here, but it turns out that these two definitions are actually the same—this is because there is an algorithm for performing field operations and taking square roots in the plane, and this algorithm involves only drawing lines and circles, starting with two rational points.
So back to what this website does: it visualizes this construction process. You enter an algebraically constructible number, and it will draw out the geometric construction process for you!