Correct! - CatenaryGatewayArch.jpg (11726 bytes)

St. Louis Arch It looks like a parabola, but it's not. The Gateway Arch in St. Louis, Missouri is an inverted catenary. A catenary is the curve of a hanging chain. (See the hanging chain images below.) Galileo thought this curve was a parabola, so don't feel bad if you were also fooled. The catenary shape minimizes the potential energy throughout the chain. When shifted, a hanging chain will naturally return to this position. At each point in a hanging chain or arch, the opposing forces (chain: tension forces, arch: compression forces) are balanced. This creates stability.

The catenary equation is  where a is determined by the linear density and tension of the chain. This is a transcendental curve rather than an algebraic curve like the parabola. The catenary is a hyperbolic function: .

Compare these three chains. They all form the catenary shape.
chain-long-heavy.JPG (6180 bytes)  chain-thick-wide.JPG (6162 bytes)  chain-long-thin.JPG (3496 bytes)
Each was photographed against the same wall. Use the cracks between boards to compare sizes. (Thanks to my family for helping me with these.)

Want to learn more?
Keep reading and follow the links below.

Famous Curves Index: Catenary
Diagram, history, and connections to other curves.

Hanging with Galileo
Suspension bridges and the parabola. Hanging Chains and the catenary.

The Catenary: A Curve of Low Potential Energy
An activity for students to compare parabolas with hanging chains, calculate potential energy, and find the equations of the Gateway Arch.

Build an Arch
Understanding the catenary arch and its strength.

The Catenary: The Statics of a Hanging Chain
Geometry, physics, and differential equations.

Jefferson National Expansion Memorial Gateway Arch
Architecture in the Parks: A National Historic Landmark Theme Study
Jefferson who? Gateway to what? Why is the arch unique in American architecture?

Arch History & Architectural Information
Historical and architectural overview including equations, materials, and construction. Compare the Gateway Arch to other monuments.

Other Resources
e: The Story of a Number by Eli Maor, 1994.
Gateway Arch picture from http://www.bluffton.edu/~sullivanm/stlsaar/stlsaar.html


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Abby Brown - Torrey Pines High School - April 2002