Give me your tired, your poor, Your huddled non-mathematicians, yearning to breathe free

Here we have a pentagon with 5 equal sides, and all its diagonals drawn in. This diagram is actually made up of pieces with 4 different lengths. One piece is colored for each of those length.
Your job, non-mathematician, is to divide the orange length by the red length, the red length by the blue length, and the blue length by the green length. You may drag the two labeled points wherever you want (make sure you can see the lengths!).

What do you notice? You are on your way to a mathematical discovery.