The Coastline Paradox

How can one coastline be two different lengths?

The coastline of Australia is thought to be roughly 12,500km long. But The World Factbook claims the figure is more than double this, at 25,700km. This ambiguity over the length of a coast is known as the coastline paradox.

The length of a coastline depends on the level of detail at which you measure it. Using a long measuring stick that sweeps across jagged stretches of coastline will give you a short coastline length. Conversely, a shorter measuring stick that enables you to measure inside every inlet along the coast will calculate a longer length of coastline. So what length of measuring stick should we use?

In this video Derek Muller relates the coastal paradox to the Koch Snowflake – a shape made from layer upon layer of equilateral triangles. This type of shape is called a fractal, which means it looks similar on many different scales.

Coastlines have a fractal structure too; when we zoom in they look roughly the same to how they do from afar. This similarity helps explain why the length of a coastline cannot be well-defined.    

The fractal geometries found in nature were synthesized in the world's first fractal movie by animator Loren Carpenter in 1979-80.

Themes

Maths

Details

Type:
Documentary
People:
Dr Derek Muller
Published:
2012
Filmed:
2012
Credits:

Derek Muller

 

Collections with this video:
Veritasium

Licence: Standard YouTube Licence

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