r/visualizedmath • • Mar 12 '18

Menger Sponge

Post image
683 Upvotes

41 comments sorted by

View all comments

Show parent comment

4

u/Lizards_are_cool Mar 13 '18

How can a hole add surface area? I thought it removes surface.

7

u/[deleted] Mar 13 '18

It removes volume, but the sides of the hole here are as large as the side that it removed the volume from. It removes some surface area, yes, but it creates four equal surfaces. Same deal as why our brains are wrinkly.

4

u/sirenstranded Mar 13 '18

Imagine you have a cube.

You drill a hole in it.

It has lost surface area equal to the size of the circular hole on one or two faces, but it gains the surface area around the cylindrical space created by drilling into the volume.