What is the arclength of Gateway Arch?

The Gateway Arch, officially called the Gateway to the West, is a monument in St. Louis, Missouri, United States. It can be approximated as a catenary curve and its arclength can be calculated using the formula for the arclength of a catenary:

$$s = a(e^x/y)_a^b$$

where \(a\) is the horizontal distance between the endpoints, \(b\) is the vertical distance between the endpoints, and \(e\) is the base of the natural logarithm.

The Gateway Arch has a horizontal distance of 630 feet and a vertical distance of 630 feet, so the arclength of the Gateway Arch is:

$$s = 630(e^{630/630})_{0}^{630} = 630(e-1) \approx 1151\text{ feet}$$