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Everything about Pentagonal number
Figurate 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 construction of pentagonal numbers creates a pattern of inside dots that are not rotationally symmetrical. The nth pentagonal number pn is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. For instance, the third one is formed from outlines comprising 1, 5 and 10 dots, but the 1, and 3 of the 5, coincide with 3 of the 10 – leaving 12 distinct dots, 10 in the form of a pentagon, and 2 inside. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Pentagonal numberA 5-minute orientation
- Skim a recent paper: Study on multi-objective linear fractional programming problem involving pentagonal intuitionistic fuzzy numberInfluential work since 2022
- Pick up a classic book: Amulets and superstitionsThe most-reprinted book on the subject
- Read the landmark paper: The truncated pentagonal number theoremCited 106 times
- Go sideways: Pell numberA closely related topic
- Go sideways: Triangular numberA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
The truncated pentagonal number theorem
Pentagonal fuzzy number, its properties and application in fuzzy equation
The Pentagonal Bipyramid as Fundamental Structure for Compounds with the Coordination Number Seven
Euler's Pentagonal Number Theorem
A study on pentagonal fuzzy number and its corresponding matrices
A further look at the truncated pentagonal number theorem
A Pentagonal Number Sieve
Positivity and tails of pentagonal number series
🆕 Influential since 2022
Study on multi-objective linear fractional programming problem involving pentagonal intuitionistic fuzzy number
On the Kirchhoff index and the number of spanning trees of cylinder/Möbius pentagonal chain
Exploring the Atwood number impact on shock-driven hydrodynamic instability at pentagonal interface using discontinuous Galerkin simulations
A New Ranking Approach for Solving Fuzzy Transportation Problem with Pentagonal Fuzzy Number
Edge resolving number of pentagonal circular ladder
📚 Books worth reading
Amulets and superstitionsE. A. Wallis Budge · 1930
Operations ManagementRoberta S. Russell, Bernard Taylor · 1998
Working With NumbersJames T. Shea · 1987
The Conspirators HierarchyJohn Coleman · 1992
Beautiful GeometryEli Maor, Eugen Jost · 2014
The Genius of EulerWilliam Dunham · 2007
100 Essential Things You Didn't Know You Didn't KnowJohn D. Barrow · 2009- 📕Teach Yourself Mechanical DraughtsmanshipS. M. Hood · 1952
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Pell number In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational…
- Triangular number The triangular numbers or triangle numbers are the sequence of positive integers that can be represented as a lattice of points arranged in an equilateral…
- Tetrahedral number A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedro…
- Centered square number In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center…
- Polygonal number In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate…
- Factoriangular number In number theory, a factoriangular number is an integer formed by adding a factorial and a triangular number with the same index. For n≥1, the nth factoriangula…
- Pyramidal number A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. The term often refers to square pyramidal numbers,…
- Centered hexagonal number In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered figurate number that represents a hexagon with…