(Yeah, I’ve pretty much given up on my titles.)
So here’s a question that you may or may not have pondered: when we write the slope-intercept equation for a line, the m in y= mx + b is our slope, right?
Why the heck do we denote it with “m”?
There’s quite a range of theories.
According to Pat from Pats’blog, the word “slope” itself is derived from the Latin root slupan for “slip.” Which makes sense when you think of what the slope actually is.
A common myth is that Descartes first used m because it was the first letter of some French word related to slope, but according to a bunch of people who speak French (and we should probably trust them about their language) the appropriate word for slope is “pente.”
Pat digs up some info from Jeff Miller, who claims that the earliest use of m dates back to 1844 when Brit Matthew O’Brien wrote “A Treatise on Plane Co-Ordinate Geometry” and Irish George Salmon published “A Treatise on Conic Sections.”
Another possibility was pointed out by John Conway, who suggested that m could stand for “modulus of slope.”
But in the end, no one’s really sure exactly when and why we got to using m for slope. I’m sure there are a fair number of mathematical symbols we use that don’t have a clear origin, but I know I’ve never really thought about m for slope before. I guess that’s because when I first learned y = mx + b I always thought m was appropriate because if you follow the trace of the letter the slope changes a whole bunch.
I was a dumb kid.
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.)
Geometry makes things so much clearer, doesn’t it?
This is FREAKING AWESOME!!!!