This interactive applet illustrates the L1, L2, and L-infinity-norms of vectors:
|x|_1 = |x1| + |x2| + |x3|,
|x|_2 = sqrt(x1^2 + x2^2 + x3^2),
|x|_infinity = max(x1,x2,x3).
Compare Mathworld on Vector Norms. You can interactively change x1, x2 and x3 by moving the red dots.
SDG. Created by Eckhard Hitzer with Cinderella