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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 3 2 and can be written as 3 × 3.
1.2 Square numbers. 1.3 Pentagonal numbers. ... Print/export Download as PDF; Printable version; ... 1 11 30 58 95 141 196 260
Geometric representation of the square pyramidal number 1 + 4 + 9 + 16 = 30. In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci.
30 is a square pyramidal number. 30 is an even , composite , pronic number . With 2 , 3 , and 5 as its prime factors , it is a regular number and the first sphenic number , the smallest of the form 2 × 3 × r {\displaystyle 2\times 3\times r} , where r is a prime greater than 3.
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
Consequently, a square number is also triangular if and only if + is square, that is, there are numbers and such that =. This is an instance of the Pell equation x 2 − n y 2 = 1 {\displaystyle x^{2}-ny^{2}=1} with n = 8 {\displaystyle n=8} .
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A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
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