Question: Information: - A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right. The th triangular number is the number of dots composing a triangle with dots on a side, and is equal to the sum of the natural numbers from 1 to . The sequence of triangular numbers , starting at the 0th triangular number, is - Geometry (from the ; "geo-" "earth", "-metron" "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. - In geometry, an octagon (from the Greek "oktagnon", "eight angles") is an eight-sided polygon or 8-gon. - In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots are thought of as alphas (units). These are one type of 2-dimensional figurate numbers. - In planar geometry, an angle is the figure formed by two rays, called the "sides" of the angle, sharing a common endpoint, called the "vertex" of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. - An octagonal number is a figurate number that represents an octagon . The octagonal number for n is given by the formula 3n2 - 2n , with n > 0 . The first few octagonal numbers are : 1 , 8 , 21 , 40 , 65 , 96 , 133 , 176 , 225 , 280 , 341 , 408 , 481 , 560 , 645 , 736 , 833 , 936 ( sequence A000567 in OEIS ) Octagonal numbers can be formed by placing triangular numbers on the four sides of a square . To put it algebraically , the n - th octagonal number is x_n = n ^ 2 + 4 \ sum -- ( k = 1 ) ^ ( n - 1 ) k = 3n ^ 2 - 2n . The octagonal number for n can also be calculated by adding the square of n to twice the ( n - 1 ) th pronic number . Octagonal numbers consistently alternate parity . Octagonal numbers are occasionally referred to as '' star numbers , '' though that term is more commonly used to refer to centered dodecagonal numbers . - The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean - The Multinational Aircrew Electronic Warfare Tactics Facility Polygone - POLYGON is an Electronic Warfare Tactics Range located on the border between Germany and France. It is a tri-national facility operated by France, Germany and the United States. 'octagonal number' is related to which object entity through the relation of 'subclass of'? Choices: - angle - diagram - facility - geometry - germany - greek - intersection - mathematics - measurement - natural - number - octagon - plane - polygonal number - range - regular polygon - sequence - shape - sum - term - type - warfare
Answer:
polygonal number