Finite Area and Infinite Perimeter

It is possible to have an object with the properties of finite area and infinite perimeter.  In this object, the sides enclose a finite region but the sides are made up of infinite pieces.

Check out the Koch snowflake.  It starts with an equilateral triangle.  Then, on the first iteration, each side is broken so that a smaller triangle can be put on.  Then, each side is broken again so that yet a smaller triangle can be put on.  This is done infinitely so that you get…

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s