math_fact: 414 is a value of n for which n^{4}, n^{5}, n^{6}, and n^{7} have the same digit sum.
trivia: 414 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
historical_date: February 17th is the day in 1913 that the Armory Show opens in New York City, displaying works of artists who are to become some of the most influential painters of the early 20th century.