Quadratic

I looked up "Parabolas in Real Life" on Google and right away I see the very famous St. Louis Arch, also called the Gateway Arch. I knew I just had to do some research on the construction of the arch, just look at it! It's absolutely amazing, and a perfect parabola (or so I first though)! I couldn't begin to understand how the managed to build such an odd structure because it looks as if the during the construction the entire thing would come crashing down. Apparently though, the arch isn't a parabola at all, it's refereed to as an inverted catenary. A catenary is defined as the "curve formed when you allow a chain or cable to hang from its two ends under its own weight", so in an inverted catenary is one in which the curve hangs up instead of down. 


By observing the construction below I was able to conclude that each leg had to essentially support its own weight until they came close to touching each other. In the 5th picture we see a brace added to the middle that made it so neither side would collapse. Wedges, that could be compared to triangular wedges of cheese, were stacked one on top of the other until the two curves finally met in the middle. There was lots of math involved in the creation of the Gateway and although I don't really understand a lot of it....

The geometric form of the structure was set by mathematical equations provided to Saarinen by Hannskarl Bandel. Bruce Detmers and other architects expressed the geometric form in blueprints with this equation:^[72]

,

with the constants

where f_c = 625.0925 ft (191 m) is the maximum height of centroid, Q_b = 1,262.6651 sq ft (117 m²) is the maximum cross sectional area of arch at base,Q_t= 125.1406 sq ft (12 m²) is the minimum cross sectional area of arch at top, and L = 299.2239 ft (91 m) is the half width of centroid at the base.

(copied from wikipedia)

it is clear that without a lot of time and thought this project would have gone nowhere. It's very cool to see how such a daunting project to light and how it was made!