Persona 3 Reload: Which spiral is not an algebraic spiral?

If you thought history class was difficult in Persona 3 Reload, just wait for 4/27, and your first math lesson with Ms. Miyahara. If you can’t tell the difference between an algebraic spiral and a pseudo-spiral just by looking at them, you’re going to need help.

Which of the following is not an algebraic spiral?

I don’t remember which answer I gave, but it wasn’t A, which is the correct answer. Yes, spiral A is not an algebraic spiral, while the other three spirals are. As Ms. Miyahara goes on to explain, you can graph an algebraic spiral using an algebraic equation. So, A is obviously the answer, right? No. No, I still don’t understand.

If you’re staring at the same four diagrams in the screenshot above and scratching your head in despair, don’t worry, you’re not alone. It’s a long time since I left school, but I’m pretty sure I never learned anything like this.

After some research, I did find an explanation of the difference between an algebraic spiral and a pseudo-spiral, but it was no help at all. Apparently, the equations of algebraic spirals are algebraic with respect to ρ and ϕ. Whereas the equations of pseudo-spirals are always r = as^m, with r being the radius of curvature, and s being the arc length.

So, that clears that up then, right? No, of course not. This explanation brought me no closer to the answer, and frankly, I was starting to get a bit ρissed ϕff. I was pretty sure that B was an Archimedean spiral, which is a type of algebraic spiral. But I had no idea how to identify the imposter among the other three spirals, all of which look a bit sketchy, to be honest.

The good news is, unlike the Jomon period from Mr. Ono’s history class, Ms. Miyahara’s spirals do not come up in the Persona 3 Reloaded midterms. So, you can select A, shrug your shoulders, earn the respect of your classmates, and forget the whole thing. I’ll tell you one thing: I’ll never look at a cinnamon swirl in the same way again.