Let's explore the word, "pen."
The word is found in the word, "pencil," which is a long writing utinsel full of graphite/lead. It is also found in the word, "pen," which by itself generally refers to a long writing utensil that uses ink as a means of lubricative physical recording. The word is also found in the word, "penis," which is a sexual organ used by a man to write his genetic history upon the women he encounters.
Is it coincidence?
I don't think so.