Warren Beatty moved his family from Richmond to Norfolk and then to Arlington and Waverly, then back to Arlington, eventually taking a position at Arlington's Thomas Jefferson Junior High School in 1945. During the 1950s, the family resided in the Dominion Hills section of Arlington. Beatty's elder sister is the actress, dancer and writer Shirley MacLaine. His uncle, by marriage, was Canadian politician A. A. MacLeod. Beatty became interested in movies before his teens, when he often accompanied his sister to theaters. One film that had an important early influence on him was "The Philadelphia Story" (1940), which he saw when it
Beatty sequence then formula_4 is also a positive irrational number. These two numbers naturally satisfy the equation formula_5. The two Beatty sequences they generate, form a "pair of complementary Beatty sequences". Here, "complementary" means that every positive integer belongs to exactly one of these two sequences. For "r" = the golden mean, we have "s" = "r" + 1. In this case, the sequence formula_8, known as the "lower Wythoff sequence", is and the complementary sequence formula_9, the "upper Wythoff sequence", is These sequences define the optimal strategy for Wythoff's game, and are used in the definition of the Wythoff array As