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One is the "Gateway To The West" arch in St. Louis, Missouri. It is also possible McDonalds Restaurants have a double inverted catenary arch shape. It resembles a letter M in script form.
The Jefferson National Expansion Memorial, The Gateway Arch, is located in St. Louis, Missouri.
yes
No shape is mathematical really unless it has been created by a mathematical formula, but is certainly a geometric shape. But anything which is a 2D or 3D shape is geometric. My improvement: A catenary curve from a mathematical equation such as cosh x, is a mathematical and natural shape. Maby each other arch can be approximated by a mathematical formula.
triangles are the second strongest shape next to the arch