According to the Owner's Manual for the Gateway Arch by William Thayer, the construction made use of the following mathematical equation.
y(x) = a + b * cosh( c * x)
a= 693.8597 b= -68.7672 c=.010033
-299.2239
Cross-sections of the arch are equilateral triangles, and (x,y) traces teh path of the centers of mass of the triangles whose area is given by the following equation:
A(x) = d * cosh (c*x)
d = 125.1406
1. Plot this expression and confirm its shape
2. Find the height to the top most point and the width at the base and mid-height.