How Do You Spell POLYGONAL NUMBERS?

1. Polygonal numbers are a class of figurate numbers that can be represented as regular, closed polygons in a two-dimensional plane, each having a specific number of sides or vertices. These numbers are generated by a geometric pattern, where each term is derived based on the properties of the corresponding polygon.

   The term "polygonal" refers to the shape of the numbers, which is a polygon. A polygon is a closed figure consisting of straight line segments joined together to form a loop. The sides or edges are the line segments, and the vertices are the points where the line segments meet. Each polygonal number is associated with a specific polygon, such as triangles, squares, pentagons, hexagons, and so on.

   To create polygonal numbers, the formula used depends on the number of sides or vertices of the associated polygon. For example, triangle numbers can be found using the formula n(n+1)/2, square numbers can be calculated as n^2, and pentagonal numbers follow the formula n(3n-1)/2, where n represents the term or position of the number in the sequence.

   Polygonal numbers have been studied extensively in mathematics, and they have various applications in number theory, geometry, and combinatorics. They often exhibit interesting patterns and relationships, making them a fascinating area of exploration for mathematicians and number enthusiasts.

2. The successive sums of any series of numbers in arithmetical progression.

   Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.

Common Misspellings for POLYGONAL NUMBERS

The etymology of the term "polygonal numbers" is derived from the combination of two words: "polygon" and "numbers".

1. Polygon: The word "polygon" originated from the Greek terms "poly-" meaning "many" and "gonía" meaning "angle" or "corner". It refers to a two-dimensional geometric shape with straight sides and multiple angles or corners.

2. Numbers: The term "numbers" refers to mathematical objects used for counting, measuring, or representing quantities.

When these two terms are combined, "polygonal numbers" refers to a specific set of numbers that have a connection to polygons, specifically the representation of these numbers using geometric patterns.

The term "polygonal numbers" helps convey the idea that these numbers can be represented visually using polygonal shapes, such as triangles, squares, pentagons, hexagons, etc.