From the Super Mario Wiki, the Mario encyclopedia
The Measuring Stick is an item in the SNES and PC releases of Mario's Time Machine. It is obtained by a time-traveling Mario in Athens after he gives a Laurel Wreath to a writer: in exchange for the generous gift, the writer gives Mario a measuring stick and tells him to go see Aristotle. Aristotle, on his end, also mentions that he wants to talk more about geometry, but he has misplaced his own measuring stick. Once Mario gives him the measuring stick, he appreciates the gift and goes on to talk about the book in Mario's possession, the Republic.