Maths Blog: TracingCurves

How I taught myself calculus – Some intuitive reasoning

When I first taught myself calculus prior to more formal learning, I already had an idea of the concept of differentiation as a tool to help us measure the rate of change of a curve. I also already had some ide...

Why 0!=1 – Talking math and terminal access code decryption in No Man’s Sky

Several months ago I made a video on a particular terminal access code decrypt problem that I had come across in No Man's Sky (see above). The given sequence was 1 2 6 24 120. In order to decrypt the terminal a...

Euler’s Identity Proof

This quickly became one of my favourite derivations. And with the launch of my blog, I couldn't wait to write about it. First, an introduction. This is Euler's formula: \ When we set x = pi, this formula...

Proof of the Quadratic Formula (by completing the square)

With the launch of my new mathematics blog, I thought I would start with something of a nostalgia post: a note on the quadratic formula. The proof of the quadratic formula (by completing the square) was one ...

Binomial Expansion – A Neat Trick

There's a neat trick when it comes to binomial expansion. Perhaps 'trick' is the wrong word. It seems more like an algorithmic approach to thinking about binomial expansion that doesn't require Pascal's triangl...

Exponents, History, Civilization

I decided to make a video the other day on exponent properties. I like to think about mathematical concepts and to explore first principles. I spend a lot of my spare time working through proofs and also studyi...