[math-fun] semicircles, parabolae, catenaries
The ancient Roman's were really big into circular arches. I presume that arches were easy to draw with a string for a radius. Even the medieval churches continued to depend upon circular arcs: their windows with pointed tops used two circular arcs intersecting at the top. Somewhere along the line, parabolae became fashionable. Was it as late as the Brooklyn Bridge in the late 1800's ? Perhaps the requirement for thousands of railway bridges around the world forced the development of parabolic arches. The ancient Egyptians toyed with catenaries, but didn't really grasp the significant differences between catenaries & other kinds of arches, but they did dimly sense that they weren't the same. Catenaries seemed to finally hit the "big time" with the Sagrada FamÃlia in Barcelona in the early 20'th century, which was designed "upside down" using weights & ropes. http://en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia The ancient Romans were darn good engineers & I'm sure they didn't like to carry around more dirt & stone than was strictly necessary. Is anyone here aware of any deviation from circularity in any ancient Roman structures? Also, the Romans developed the use of concrete to a high art in the 2nd & 1st centures B.C.E. Did they ever utilize strengthening members -- e.g., "rebar"-like members?
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Henry Baker