For 10 points, identify this man who names an object that has only one side which is formed by taking a piece of paper, twisting it, and then gluing the ends together, his namesake strip.
The function named after this man is equal to zero for non square-free numbers, one for numbers with an even number of prime factors and negative one for numbers with an odd number of prime factors. A statement involving summing over divisors that uses the aforementioned function is his namesake inversion formula. The orientability of a surface is determined by whether it contains a subset homeomorphic to an entity named after this man, which when glued to itself forms a Klein bottle. For 10 points, identify this man who names an object that has only one side which is formed by taking a piece of paper, twisting it, and then gluing the ends together, his namesake strip.
The function named after this man is equal to zero for non square-free numbers, one for numbers with an even number of prime factors and negative one for numbers with an odd number of prime factors.
August (Ferdinand) Mobius