Final answer:
Verne and Irene Castle were significant to the dance world for popularizing modern ballroom dance in the 20th century, refining dancing etiquette, and influencing fashion and music. They were also trendsetters who introduced new dance concepts and made dance more accessible to the public.
Step-by-step explanation:
Verne and Irene Castle are significant to the dance world because they helped popularize modern ballroom dancing in the early 20th century. They introduced a more refined and elegant style that contrasted with the ragtime dances of the period. Their influence extended beyond dance moves to affect social dancing etiquette, fashion, and music.
The Castles were responsible for elevating social dance to a new level of respectability and popularity. This was achieved in part through their performances on stage and in films, as well as by teaching dance to a broader public. They established dance schools and wrote instructional books, making dance accessible to many people and ensuring its spread and evolution.
Moreover, they were trendsetters who also transformed the way people danced together. With the Castles, dance became a more intimate and personal form of expression. They introduced concepts like dancing closer together and using simpler steps set to ragtime music, which were considered revolutionary at the time.