Photography

In order to better understand a space we often impose a coordinate system on it.  This allows us to study the characteristics of that space in particularly mathematical ways, like through distance, area, and curvature.

Looking at the city through this rectangular mesh put me in mind of this process of coordinatization, and highlights how the coordinate system is indeed an abstraction from reality and an active choice we make.

Here’s a demonstration of a theorem of elementary geometry:  if parallel lines divide one transversal into congruent parts, then they divide all transversals into congruent parts.

Here, it’s easy to see that the top rail, the one perpendicular to the parallel posts, is divided into equal parts by the vertical posts.  So the angled segments are divided into congruent parts as well.