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I hope not! The Terrible Towel came into being in 1975 and the last manned visit to the moon was in 1972.
I never heard of the "terrible towel", but basically you take square roots of numbers and measurements, not of objects.
Yes there has.
In a circle.
McArthur Towel and Sports Co. is the current manufacturer of the Terrible Towel. The company is located in Baraboo, Wisconsin.