Editing Square pyramidal number (section)

==History==
The pyramidal numbers were one of the few types of three-dimensional figurate numbers studied in [[Greek mathematics]], in works by [[Nicomachus]], [[Theon of Smyrna]], and [[Iamblichus]].{{r|federico}} Formulas for summing consecutive squares to give a cubic polynomial, whose values are the square pyramidal numbers, are given by [[Archimedes]], who used this sum as a [[Lemma (mathematics)|lemma]] as part of a study of the volume of a [[cone]],{{r|archimedes}} and by [[Fibonacci]], as part of a more general solution to the problem of finding formulas for sums of progressions of squares.{{r|fibonacci}} The square pyramidal numbers were also one of the families of figurate numbers studied by [[Japanese mathematics|Japanese mathematicians]] of the wasan period, who named them "kirei saijō suida" (with modern [[kanji]], 奇零 再乗 蓑深).{{r|yanagihara}}

The same problem, formulated as one of counting the [[cannonball]]s in a square pyramid, was posed by [[Walter Raleigh]] to mathematician [[Thomas Harriot]] in the late 1500s, while both were on a sea voyage. The [[cannonball problem]], asking whether there are any square pyramidal numbers that are also square numbers other than 1 and 4900, is said to have developed out of this exchange. [[Édouard Lucas]] found the 4900-ball pyramid with a square number of balls, and in making the cannonball problem more widely known, suggested that it was the only nontrivial solution.{{r|parker}} After incomplete proofs by Lucas and Claude-Séraphin Moret-Blanc, the first complete proof that no other such numbers exist was given by [[G. N. Watson]] in 1918.{{r|anglin}}