The e-Octagon

I just found this and I am happy.

If you have a unit circle, you have an area of π square units.

If you inscribe a regular pentagon in the unit circle, and then add triangles in 3 of the circle segments as shown:

The blue area in the resulting octagon will be 2.7144 square units.

This is a good approximation of the value of e, 2.71828.

This symmetrical, irregular octagon is a good visual comparison between π and e.