pentagonal number
1Pentagonal number — A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The n …
2Pentagonal number theorem — In mathematics, the pentagonal number theorem, originally due to Euler, relates the product and series representations of the Euler function. It states that:prod {n=1}^infty (1 x^n)=sum {k= infty}^infty( 1)^kx^{k(3k 1)/2}.In other words, :(1 x)(1 …
3Centered pentagonal number — A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for n is given by the formula …
4Pentagonal pyramidal number — A pentagonal pyramidal number is a figurate number that represents the number of objects in a pyramid with a pentagonal base.MathWorld|title=Pentagonal Pyramidal Number|urlname=PentagonalPyramidalNumber] The n th pentagonal pyramidal number is… …
5Number theory — A Lehmer sieve an analog computer once used for finding primes and solving simple diophantine equations. Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers (the… …
6number game — Introduction any of various puzzles and games that involve aspects of mathematics. Mathematical recreations comprise puzzles and games that vary from naive amusements to sophisticated problems, some of which have never been solved.… …
7number symbolism — Introduction cultural associations, including religious, philosophic, and aesthetic, with various numbers. Humanity has had a love hate relationship with numbers from the earliest times. Bones dating from perhaps 30,000 years ago show …
81000 (number) — List of numbers Integers ← 1k 2k 3k 4k 5k 6k 7k 8k 9k → Cardinal 1000 one thousand …
92000 (number) — 2000 (two thousand) is the natural number following 1999 and preceding 2001.See also: millennium, year 2000 AD, Y2K, 2000 (disambiguation).Two thousand is the highest number expressible using only two unmodified characters in roman numerals… …
10Partition (number theory) — Young diagrams associated to the partitions of the positive integers 1 through 8. They are so arranged that images under the reflection about the main diagonal of the square are conjugate partitions. In number theory and combinatorics, a… …
