# Terminal Velocity in a Vacuum

It is commonly claimed that an object dropped in a vacuum will continue to accelerate indefinitely, reaching arbitrarily high speeds. In fact, even in a vacuum, a falling object has a maximum speed it can reach. In essence, this is the terminal velocity in a vacuum.

# Reflecting on the Reflection Principle

From finance to route planning, the reflection principle is an incredibly versatile technique, capable of transforming seemingly fiendish problems into elegant systems. In this post, I walk through three example applications of the principle.

# Efficient Calculation of Efficient Frontiers

The efficient frontier is a ubiquitous tool in quantative finance, yet it is often calculated using incredibly inefficient methods. Can we do better using a healthy helping of analysis and linear algebra.

# A Polish Approach to Countdown

The Countdown numbers game is notoriously fiendish. That said, with the right computational tricks, it can be solved using only basic coding abilities.

# The Look-and-Say Sequence: A Tribute to John Conway

One week ago today, we lost one of the most inspirational mathematicians of this generation. In this post, we take a brief look at the incredible legacy that John Conway left behind. On top of that we will discuss one of the many problems he tackled during his career; one that, to this day, occupies a special place in my heart. We close by discussing an intriguing puzzle that I am yet to find a solution to—can you?

Deciding the winner of a round-robin tournament is no simple task. The most naïve approach can easily be faltered by the existence of $k$-paradoxical tournaments. But what are these tournaments and what do we know about them? There is surprisingly little discussion on the topic and so, in this post, I plan to collate various pieces of knowledge on the subject into one succinct guide.