____ /\ \ ____/ \___\ /\ \ / / ____/ \ \/___/ /\ \ \ \ ____/ \ \ \_______\ /\ \ \ \ / / / \ \ \ \/_______/ \ \ \ \ \ \ \ \ \___________\ \ \ \ / / \ \ \/___________/ \ \ \ \ \_______________\ \ / / \/_______________/ x 3 = ________________ /\ \ ____/ \____ \ /\ \ / /\ \ / \ \/___/ \____ \ / \ \ / /\ \ / \ \/___/ \____ \ / \ \ / /\ \ / \ \/___/ \___\ / \ \ / / / \_______________\/___/ \ / / / \ / ____/ / \ / / / \ / ____/ / \ / / / \ / ____/ / \ / / / \/___/_______________/

b) sum of the first n squares = n(n+1)(2n+1)/6

ok, i guess i'll need some words now. six copies of the "square pyramid" pack an n x (n + 1) x (2n + 1) box, whence the formula. there are six such blocks in the math common area at smith college, where i learned of this construction. i later saw a similar, or perhaps the same construction, i believe as a "proof without words" in math intelligencer. (i'm not sure which came first.) i don't have the reference at my fingertips; perhaps someone can find it. (it's also possible that the intelligencer proof only used 3 pyramids, then sliced and re-assembled to get an n x (n + 1) x (n + 1/2) block.) mike