# Summer of Math Exposition

SoME3

You can find the SoME3 winners below. The full list of non video entries is available here. The playlist of all video entries is available here

## The 5 winners are

### The Mathematics of String Art

String Art recreates an image using string. An algorithm is used to calculate the order in which the string needs to be wrapped around the nails. This video is about the mathematics behind this algorithm.

### Minimal Surfaces & the Calculus of Variations

Bubbles naturally try to minimize surface area, and so for a given boundary, what is that surface that is formed? In this video we will derive the Euler-Lagrange equation from the Calculus of Variations and apply it to derive the formula for a catenoid that is formed my making a bubble between two parallel rings.

### Pixel Art Anti Aliasing

A full walkthrough of the motivation, background, derivations, and implementation of an efficient anti-aliasing filter for rendering pixel art.

### Rethinking the real line

We take a geometric approach to rational numbers, to rethink how to organize the real line. Along the way, we visualize Diophantine approximation and continued fractions. And your favourite number, pi.