Take out a sheet of paper and a pen or pencil. Draw 3 random lines across the page. You should see one closed polygon with three corners.
Now draw another line. How many polygons do you see? How many corners do they have?
Draw a fifth line. How many polygons do you see? How many corners do they have?
Five randomly drawn lines. There are four closed polygons. Two polygons have three corners. One has four corners, and the last has five corners.
Inspired by the Quanta article “Scientists Uncover the Universal Geometry of Geology” I set out to create my own simulation of the same experiment above. Since it takes at least three lines but could have infinitely many on a page, I ran my experiment from three lines to ten lines. The average as a function of lines drawn is shown below. The average number of corners or edges is six, just as the article mentioned.