Recently the "Batman Equation" has been memetically propagating around the Internet.
the work of a user on Reddit.
I liked it enough to try to make my own. There are a few tricks to this process. First break the shape up into curves that you can easily write equations for, of the form f(x,y)=0.
equation I used for plotting.)
The final plot looks like this:
It is remarkable how well a single ellipse traces out the outer edge of a banana silhouette. I checked a couple of other bananas, and they also have this property. I finally went to a grocery store and sifted through all their bananas to find the least elliptical one I could:
From the red sample points along the edge, I found that even this banana was almost well-approximated by an ellipse.
It is the first three data points that make this an exception to Bananagrammer's First Law of Bananas:
The outer edge of the longitudinal section of a banana follows an elliptical path, with the banana's stem being roughly on the end of the ellipse's long axis.
The question to ask at this point is, "Why are bananas shaped the way they are?". The simple answer is that when a bunch of bananas start growing on a tree, they are initially pointing more down than up. As they become larger, they curve up toward the sun. A banana's exact shape will therefore depend on where it is with respect to its neighbors.
A full explanation of why bananas are so elliptical will require more investigation. People who want to give me research grants are welcome to do so. Actually, everybody is welcome to do so. To everyone else, tune in next week. Same Banana-time, same Banana-channel!