I was making one of my daily green smoothies the other day, and while washing the kale, I stopped as I often do to ponder the fascinating leaves. I have long marveled at the pure beauty of kale- deep green and infinitely crinkly on the edges- and I wondered if anyone has ever measured the edge of a kale leaf. It’s an extremely intricate edge, and seems to go on forever. I googled it, but no luck. The fractal beauty, nonetheless, took me on an odyssey of just how special kale really is, beyond its incredible health benefits. Now, presumably you know the health benefits of kale. There’s quite a nutritional kick, including tons of Vitamin K (great for brain health), more bioavailable calcium than milk, and enough iron and protein for it to have been dubbed “the new beef“. But did you know that kale’s edges illustrate a beautiful mathematical concept called “hyperbolic geometry” (HG)? HG is a non-Euclidean geometrical concept that can flatten a sphere into two dimensions. Here is an illustration of hyperbolic geometry:
This can also be seen in some of the works from one of my favorite artists, M. C. Escher:
Euclidean geometry is the most practical geometry for everyday applications, of course, but researching kale led me to discover non-Euclidean geometry and hence hyperbolic geometry (the other main non-Euclidean geometry is spherical/elliptical). The thing that fascinates me about this is that it deviates from the usual… kinda the way chaos and string theory fascinate me. The sum of the sides of a hyperbolic triangle add up to less than 180 degrees. It has been used to illustrate the possible curvature of space (although I just read that the most recent information tells us that the universe is pretty flat. At least this one is. Who knows about the others in the multiverse? Lol!). I am still looking for a measurement of a kale leaf’s perimeter… and did you know that October 2nd was National Kale Day? And to end, here is a fractal illustration of kale:
This picture is actually on a t-shirt!! Lol!