Ads
related to: triangle polygonal numberskutasoftware.com has been visited by 10K+ users in the past month
Search results
Results from the WOW.Com Content Network
In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon [1]: 2-3 . These are one type of 2-dimensional figurate numbers . Polygonal numbers were first studied during the 6th century BC by the Ancient Greeks, who investigated and discussed properties of oblong , triangular , and square numbers ...
The three triangular numbers are not necessarily distinct, or nonzero; for example 20 = 10 + 10 + 0. This is a special case of the Fermat polygonal number theorem. The largest triangular number of the form 2 k − 1 is 4095 (see Ramanujan–Nagell equation).
a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r = 2) or a polyhedral number (for r = 3). a member of the subset of the sets above containing only triangular numbers, pyramidal numbers , and their analogs in other dimensions.
In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n-gonal numbers.That is, every positive integer can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of five or fewer pentagonal numbers, and so on.
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
which tells us that 10 is both triangular and centered triangular, 25 is both square and centered square, etc. Whereas a prime number p cannot be a polygonal number (except the trivial case, i.e. each p is the second p-gonal number), many centered polygonal numbers are primes.
A simple polygon is monotone with respect to a line L, if any line orthogonal to L intersects the polygon at most twice. A monotone polygon can be split into two monotone chains. A polygon that is monotone with respect to the y-axis is called y-monotone. A monotone polygon with n vertices can be triangulated in O(n) time.
a number n in a pentagon is equivalent to "the number n inside n squares, which are all nested." etc.: n written in an (m + 1)-sided polygon is equivalent to "the number n inside n nested m-sided polygons". In a series of nested polygons, they are associated inward. The number n inside two triangles is equivalent to n n inside one triangle ...
Ads
related to: triangle polygonal numberskutasoftware.com has been visited by 10K+ users in the past month