<s>[INST] Describe the condition for a curve to be rectifiable between two points. [/INST] A simple curve is said to be rectifiable if there exists a positive number M such that the length of the inscribed polygonal path Π(P) ⁢ is less than M for all possible partitions P of [a,b]</s>\ <s>[INST] What are some applications on rectifiable curves in mathematics? Are there some other applications outside of mathematics? [/INST] 