I went into a physics classroom today and saw this equation written on the board:
$$ E = \frac \sigma \epsilon $$
At first I thought it referred to the electric field $ E $ between 2 parallel plates of charge density $\sigma$ separated by a material of permittivity $\epsilon$. However, I then realised it was actually the definition of the Young's Modulus $E$ for a material that has a strain $\epsilon$ when a stress $\sigma$ is applied to it!
So the same equation has two completely different meanings in two completely different areas of physics, with the symbols defined differently (ignoring symbols to show which variables are vectors etc). Is this just a coincidence resulting from the huge number of 3-variable equations in physics, or have the symbols intentionally been defined like this? Is there a deeper meaning? Are there other examples like this?