Adaptive random testing (ART) aims at enhancing the testing effectiveness of random testing (RT) by more evenly spreading test cases over the input domain. Many ART methods have been proposed, based on various, different notions. For example, distance-based ART (DART) makes use of the concept of distance to implement ART, attempting to generate new test cases that are far away from previously executed ones. The Euclidean distance has been a popular choice of distance metric, used in DART to evaluate the differences between test cases. However, is the Euclidean distance the most suitable choice for DART? To answer this question, we conducted a series of simulations to investigate the impact that the Euclidean distance, and its many variations, has on the testing effectiveness of DART. The results show that when the dimensionality of the input domain is low, the Euclidean distance may indeed be a good choice. However, when the dimensionality is high, it appears to be less suitable.