# Leif Metcalf's Website

## The Gemini Protocol

Gemini (https://gemini.circumlunar.space/docs/specification.gmi) is a new network protocol for the 'small internet'. It doesn't support inline links or images, and explicitly forbids any extensions to the protocol.

I've created a gemini server at gemini://noats.nz (source code at https://git.sr.ht/~leif/noats.nz) and my posts from now on will be posted there only. Eventually I want to duplicate my posts across https and gemini, and to run both services on the same domain.

## Geometric proof of $\sin 2\theta = 2 \sin \theta \cos \theta$

To start with, let's draw the standard trigonometric unit circle diagram for the angles $\theta$ and $2\theta$:

## Advent of Code Day 1 — Mathematica

The first task of day 1 was to find a pair of numbers in a given list that sum to 2020:

Intersection[input, 2020 - input]