R= (a/2) ^2 + B^2 _____________ 2B A=width B=Width
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No, the formula is far from simple - requiring elliptical integrals.
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.
An arch works by transfering the load on the central portion of the arch outward and downward into the columns which support it.
An arch or lintel supported by corbels, or protrusions from a wall.
The Jefferson National Expansion Memorial, The Gateway Arch, is located in St. Louis, Missouri.