Fatto matematico: 724 is the number of different arrangements of 10 non-attacking queens on an 10×10 chessboard.
Trivia: 724 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Data storica: December 24th is the day in 563 that the Byzantine church Hagia Sophia in Constantinople is dedicated for the second time after being destroyed by earthquakes.