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Square number. Square number 16 as sum of gnomons. In mathematics, a square number or perfect square is an integer that is the square of an integer; [ 1 ] in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3.
By convention, 1 is the first polygonal number for any number of sides. The rule for enlarging the polygon to the next size is to extend two adjacent arms by one point and to then add the required extra sides between those points. In the following diagrams, each extra layer is shown as in red.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
All centered square numbers are odd, and in base 10 one can notice the one's digit follows the pattern 1-5-3-5-1. All centered square numbers and their divisors have a remainder of 1 when divided by 4. Hence all centered square numbers and their divisors end with digit 1 or 5 in base 6, 8, and 12.
Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits. Hexadecimal: Base 16, widely used by computer system designers and programmers, as it provides a more human-friendly representation of binary-coded values.
Square (algebra) 5⋅5, or 52 (5 squared), can be shown graphically using a square. Each block represents one unit, 1⋅1, and the entire square represents 5⋅5, or the area of the square. In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation.
The difference of the n-th and the (n+1)-th consecutive centered k-gonal numbers is k(2n+1). The n-th centered k-gonal number is equal to the n-th regular k-gonal number plus (n-1) 2. Just as is the case with regular polygonal numbers, the first centered k-gonal number is 1. Thus, for any k, 1 is both k-gonal and centered k-gonal.
The symbol # is known variously in English-speaking regions as the number sign, [1] hash, [2] or pound sign. [3] The symbol has historically been used for a wide range of purposes including the designation of an ordinal number and as a ligatured abbreviation for pounds avoirdupois – having been derived from the now-rare ℔.