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In the neighborhood

Q.25: |
Q.31: Can you infer fencepost (or bridge^{*}) “shapes” just by walking past them? |

Okay, the question is somewhat unusual , but by *shape* I mean the cross section of each post. I've now left the house behind, and have an unusual *inverse problem* to consider. When walking around the neighborhood or driving in the countryside you will see various fences on the side of the road some of which may be made of posts with rectangular cross sections and others with circular cross sections. Of course if you are driving at more than 5 mph it's probably not easy to tell one from the other and why would you want to know anyway? We'll leave one answer to that question until later. Also, at the perimeter of playing fields, stadium's, or sometimes on roofs, one sometimes notices wire netting or mesh and at a distance the separate wires are indistinguishable from one another so the mesh looks like a sheet of uniformly gray glass. Looking at it from an increasingly acute angle (relative to the pla....*very thin* slats , it would remain equally dark at every angle (we could also visualize this question in terms of the slats in a vertical blind). Obviously, the effect of arbitrary rectangular cross sections will affect this last result in general so let us investigate these statements and try to justify them geometrically. This (and also question 32) is one of those pesky *inverse problems* mentioned in the introduction.