While I was watching a video from one of my favorite YouTube channels, I decided I wanted to try the math(s) that Professor Merrifield was describing to explain Gamma / the Lorentz factor. I’m very excited that my new blog supports $\LaTeX$ and MathJax so the formulas actually turn out looking the way they should.
While this math might look difficult at first, it is really easy. It is essentially just using the Pythagorean theorem to isolate the relationship between $t$ and $\tau$, which is the factor by which time (and length, and mass) changes for a moving object.