Quadrature of the Lune

When they snagged the tips of my snowshoes a few days ago, I cursed them. Today, in a more expansive mood, I stopped to admire their faded purple color and curvilinear form. Black Raspberries (Rubus occidentalis). The fruit a favorite treat in summer. The canes form an impenetrable thicket, arching and looping every which way. And in winter, without leaves, the canes create against a backdrop of snow a kind of geometer's junkyard filled with snippets of circles and straight lines. This reminds me of the rather arcane essay about Hippocrates' quadrature of the lune I'd read earlier in the day.

A lune is a crescent formed by the arcs of two different-sized circles, the small one peeking out from behind the big one. Hippocrates of Chios (470 - 410 BCE) was able to square this lune, that is he was able to construct a square with the same area using only a straight edge and compass. This was the first curved area to have its area calculated using geometry. One hopes Hippocrates might have been rewarded with Mt Ida Raspberries (Rubus idaeus).

"On the typographic bushes of the poem down a road leading
neither out of things nor to the mind, certain fruits are composed
of an agglomeration of spheres plumped with a drop of ink."
– Francis Ponge, from 'The Blackberries'

Posted on January 17, 2017 05:29 AM by