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A barber's pole is a type of sign used by barbers to signify the place or shop where they perform their craft. The trade sign is, by a tradition dating back to the Middle Ages, a staff or pole with a helix of colored stripes (often red and white in many countries, but usually red, white, and blue in the United States).
The foul pole is just a continuation of the line only in the air. Since it is fair if it hits the foul line, naturally it will be fair when it hits the foul pole (a continuation of the foul line. I'm sure they had to come up with the foul pole because they tried drawing a line in midair but it failed to stay =X.