Wednesday, February 27, 2019

Fuzzy Structures

 Tried to prove a conjecture today only to realize that an ortho-convex set might not even be connected. This is something you take for granted with ordinary convexity. I still think my conjecture is true if I add "connected" to my list of assumptions, but you always have to be careful in math. Here's an example of an ortho-convex set that is not connected:

After class, I took a walk towards the fairgrounds that Laura visited yesterday. Along the way, I found this old mosque attractive:

As Laura noted, though the fair isn't until May, the construction on the fairgrounds is well underway. I was struck by this mass of scaffolding that promises to be perhaps the main gate to the grounds when all is completed. It's interesting how, with the scaffolding, the structure almost looks fuzzy: