# Can someone explain the coastal paradox and infinite shoreline theory?

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How can a finite area like Great Britain have an infinite length edge?

In: Mathematics

Imagine you and a friend are standing on a beach. You and that friend want to measure how long the beach is.

Both of you decide to measure the beach in terms of stride lengths; that is, you move your foot forwards. You agree on a rule that as each of you moves on the beach, your right foot must get wet and your left foot remain dry.

You decide to move forward 20 centimetres with every step. Your friend moves forward 10 centimetres with every step.

You will notice that your friend has to do much more walking to keep their feet on the edge than you do. (*See* [*this*](https://www.researchgate.net/profile/Terry-Marks-Tarlow/publication/268803624/figure/fig3/AS:667862427521034@1536242219962/The-Coastline-Paradox-illustrates-that-shorter-measuring-units-create-longer-coastlines.ppm) *for a graphical illustration*).

As a result, your friend measures a longer distance than you. Who is right? As it turns out, there is no clear answer.

**The shorter the units of measurement, the more small features matter in the length, and thus the longer the beach appears to be**.