# Difference between revisions of "Parabolic Bridges"

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Real Life Parabolas
Field: Algebra
Image Created By: Aaron Logan

Real Life Parabolas

Parabolas are very well-known and are seen frequently in the field of mathematics. Their applications are varied and are apparent in our every day lives. For example, the main image on the right is of the Golden Gate Bridge in San Francisco, California. It has main suspension cables in the shape of a parabola.

# Basic Description

For a detailed overview of parabolas, see the page, Parabola. However, we will provide a brief summary and description of parabolas below before explaining its applications to suspension bridges.

#### Basic Definition

You may informally know parabolas as curves in the shape of a "u" which can be oriented to open upwards, downwards, sideways, or diagonally. But to be a little more mathematical, a parabola is a conic section formed by the intersection of a cone and a plane. Below is an image illustrating this.

When you were first introduced to parabolas, you learned that the quadratic equation, $y= a(x-h)^2+ k$ is its algebraic representation (where $h$ and $k$ are the coordinates of the vertex and $x$ and $y$ are the coordinates of an arbitrary point on the parabola.

#### Suspension Bridges

Suspension Bridges are the most commonly built bridges. Known for their long spans, these bridges feature a deck with vertical supports, from which long wire cables hang above. These cables are made up of hangers that run vertically downwards to hold the cable up. The suspension cables hang over the towers until they are anchored on land by the ends of the bridges. Notably, the way these cables are hung resemble the shape of a parabola.

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