|
In mathematics, a square number or perfect square is an integer that is the square of an integer;〔Some authors also call squares of rational numbers perfect squares.〕 in other words, it is the product of some integer with itself. For example, 9 is a square number, since it can be written as . The usual notation for the formula for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name ''square'' number comes from the name of the shape; see below. Square numbers are non-negative. Another way of saying that a (non-negative) number is a square number, is that its square roots are again integers. For example, = ±3, so 9 is a square number. A positive integer that has no perfect square divisors except 1 is called square-free. For a non-negative integer , the th square number is , with being the zeroth one. The concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two square integers, and, conversely, the ratio of two square integers is a square (e.g., 4/9 = (2/3)2). Starting with 1, there are square numbers up to and including , where the expression represents the floor of the number . ==Examples== The squares smaller than 602 = 3600 are: :02 = 0 :12 = 1 :22 = 4 :32 = 9 :42 = 16 :52 = 25 :62 = 36 :72 = 49 :82 = 64 :92 = 81 :102 = 100 :112 = 121 :122 = 144 :132 = 169 :142 = 196 :152 = 225 :162 = 256 :172 = 289 :182 = 324 :192 = 361 :202 = 400 :212 = 441 :222 = 484 :232 = 529 :242 = 576 :252 = 625 :262 = 676 :272 = 729 :282 = 784 :292 = 841 :302 = 900 :312 = 961 :322 = 1024 :332 = 1089 :342 = 1156 :352 = 1225 :362 = 1296 :372 = 1369 :382 = 1444 :392 = 1521 :402 = 1600 :412 = 1681 :422 = 1764 :432 = 1849 :442 = 1936 :452 = 2025 :462 = 2116 :472 = 2209 :482 = 2304 :492 = 2401 :502 = 2500 :512 = 2601 :522 = 2704 :532 = 2809 :542 = 2916 :552 = 3025 :562 = 3136 :572 = 3249 :582 = 3364 :592 = 3481 The difference between any perfect square and its predecessor is given by the identity . Equivalently, it is possible to count up square numbers by adding together the last square, the last square's root, and the current root, that is, . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Square number」の詳細全文を読む スポンサード リンク
|