Google Earth Voyager Story: The Geometry of City Planning, Part 1

Why are so many cities laid out in grids? These grids are often made up of parallel and perpendicular lines.

What are the geometric properties of lines that make these city grids ideal for organizing a community? In this investigation we'll look at the properties of lines and we'll visit different cities around the world to explore these properties.

To see the Google Earth version of this lesson go to this link. (Best viewed in Chrome.)

To see the complete collection of Google Earth Voyager Stories from Media4Math, go to this link.

1. Introduction: Houston City Grid

The downtown section of Houston, Texas, provides a perfect example of a city grid. Watch the video and then continue to the geometric construction in part 2.

2. The Shortest-Distance Principle

One of the primary reasons that cities are laid out in grids is the geometric principle that the shortest distance between two points is a line. In the previous section you saw a geometric proof of this.

In terms of a rectangular city grid, the shortest distance from A to B is shown below. The two line segments make up the distance from A to B.

One of the primary reasons that cities are laid out in grids is the geometric principle that the shortest distance between two points is a line. In the previous section you saw a geometric proof of this.

But what about a curved path? What if a city were laid out in a circular grid? Wouldn't the distance from A to B be less?

Watch the following video, which is a hands-on activity with the TI-Nspire geometry tools. You can also use other geometry software (for example, the Desmos geometry tools, www.desmos.com/geometry).

3. City Grids: Summary

So, from our analysis, this is what we can conclude about city planning grids:

• City grids made up of straight lines take advantage of the shortest-distance principle involving lines. You want to get from point A to B in the shortest amount of time possible.
• City grids made up of curved lines are impractical. Although in some cases they can offer shorter distances than a rectangular grid, they require more energy to implement, and therefore are impractical. Also, there are plenty of cases where the straight-line grid is superior.

One thing that we haven't explored yet, but will be explored in the next Voyager Story, is the fact that city grids are made up of parallel and perpendicular lines. But this brings up another question: Why are city grids more like the figure on the left than the one on the right?

Click here to go to the next exploration.