Let’s look at the super cool ISOCHRONOUS CURVE!
This video does a good job of demonstrating that the periodic motion of an object on a (frictionless) isochronous curve has a period that is independent of where the object starts on the curve. It’s a pretty cool little thing.
Edit: OH MY GOD, A WHOLE WEBSITE ABOUT CURVES AND SHAPES
(I’m going to link to one of the pages, ‘cause it looks like the majority of the site is in French, but some of it has been translated to English. I’ve clicked through a lot of the curves using the links at the bottom and I’ve only hit English pages, so if you want to look at some curves, that might be the best way to go (unless you know French)).
And it’s exactly what it sounds like. “A squircle is a shape with properties between those of a square and those of a circle,” according to the almighty Wiki. The general equation for such as shape is (x-a)4 + (y-b)4 = r4, where (a,b) is the center of the squircle and r is the minor radius of the squircle.
A squircle is not a rounded square, which is formed by arranging four quarters of a circle and connecting the loose ends with straight lines. The equation for a squircle is simpler and more generalizable than the rounded square.
So what the heck are squircles used for, other than for amusing people with their name?
Well, apparently the shape is very useful in optics. If a light is passed through a 2-D square aperture, the diffraction pattern’s central spot can be modeled by the squircle.
Squircle dinner plates also have an advantage of their round brethren—a squircle has a larger surface area than a circle with the same radius, but will still occupy the same amount of space in a cabinet. And efficiently wedging dishware into cupboards is what science is all about!
Additional note: a squircle with unequal vertical and horizontal dimensions is called a rectellipse. That sounds like a hemorrhoid medication.
(The amount of time I spent searching for an “Rx pad generator” just to make that stupid joke is embarrassing.)