On the Maximum Arc Length of Monotonic Functions

Marc Deléglise (1) , Andrew Markoe (2)

1 CTN - Combinatoire, théorie des nombres
2 RIDER UNIVERSITY

We revisit a problem solved in 1963 by Zaanen & Luxemburg in this monthly: what is the largest possible length of the graph of a monotonic function on an interval? And is there such a function that attains this length? This is an interesting and intriguing problem with a somewhat surprising answer, that should be of interest to a broad spectrum of mathematicians starting with upper level undergraduates. The proof given by Zaanen & Luxemburg is very short and elegant but not accessible to an undergraduate. We give here a longer, but elementary, proof.

Domaines: Analyse classique [math.CA]

Marc Deléglise, Andrew Markoe. On the Maximum Arc Length of Monotonic Functions. The American Mathematical Monthly, inPress, ⟨10.4169/amer.math.monthly.121.08.689⟩. ⟨hal-02079261⟩