Using the math I learned "before"

I love all aspects of the modeling process. Talking with collaborators to understand what's going on in their biological systems, researching to understand that biological system better from both the biology-side and the modeling/math-side, building a code to simulate or understand the biological system, investigating the resulting data to see what additional questions or answers arise, and the troubleshooting.

One of my recent models showed an interesting phenomena where the distribution of distances of the "spread" or stretch of the protein Obscurin was normal in x and normal in y when simulated in 2D, but was skewed in x and normal in y and z when simulated in 3D. This model is purely Monte Carlo, so randomly generated data based on a certain set of equations/rules for the geometry of the protein, which means I'd expect the spread in x, y, and z to be normally distributed with the same mean and standard deviation. It wasn't- so time to debug and understand what I did.

This is where I began using the math I learned "before." In high school, and college, where we had to learn all about domains and ranges of functions and I thought "why would I ever need to know this?" In this case, I have a bunch of trig functions that have a given domain from binomial or normal distributions (parameters set by the biology), which influences the resulting range. Noticing things like how a bimodal histogram of angles results in a skewed right distribution of cos values, and a bimodal distribution of sin values. I don't remember seeing this in a textbook, but it's pretty cool to use statistics, trig, and calculus all in one go to debug and understand the model.

Does this quick analysis answer my question: is it "right" that the x spread distribution in 3D doesn't have the same mean and standard deviation as the y and z spreads? Nope- now it's time to go back and check my modeling assumptions and double check my equations in 2D versus in 3D...