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.
But 10 cannot be arranged as a square. The number 9, on the other hand, can be (see square number):
Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number):
By convention, 1 is the first polygonal number for any number of sides. The rule for enlarging the polygon to the next size is to extend two adjacent arms by one point and to then add the required extra sides between those points. In the following diagrams, each extra layer is shown as in red.
Triangular numbers
Square numbers
Polygons with higher numbers of sides, such as pentagons and hexagons, can also be constructed according to this rule, although the dots will no longer form a perfectly regular lattice like above.
Polygonal Number - Formula to find nth Polygonal Number - Derivation
Derivation of Formula to find nth polygonal number. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtube.com/MathsSmart
published: 15 Feb 2014
Polygonal Numbers - Introduction and method to find next polygonal number
Learn about polygonal Numbers a topic of Number Theory. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtube.com/MathsSmart
published: 15 Feb 2014
Polygonal Numbers
http://demonstrations.wolfram.com/PolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., numbers to an n -gon for arbitrary positive integer n. The diagram graphically illustrates the process by which the k th n -gonal number is generated.
Contributed by: Eric W. Weisstein
published: 11 Jul 2009
(Tutorial) (Reasoning) Polygonal Numbers - Mathematics In the Modern World
published: 16 Dec 2023
Polygonal Numbers - Geometric Approach & Fermat's Polygonal Number Theorem
I created this video with the YouTube Video Editor (http://www.youtube.com/editor)
published: 09 Apr 2013
Polygonal Number Similarity
This playlist contains proofs without words and visualizations of various figurate numbers and relationships among figurate numbers. Polygonal numbers (e.g., triangular, square, pentagonal, hexagonal, heptagonal, octagonal numbers) and centered polygonal numbers (e.g., hex numbers) along with other types of figurate numbers (e.g., star numbers) are also considered.
published: 11 Jan 2021
Number of Diagonals In a Regular Polygon - Geometry
This geometry video tutorial explains how to calculate the number of diagonals in a regular polygon such as a square, pentagon, hexagon, heptagon, and an octagon. It also explains how to confirm the answer by drawing the diagonals in a regular polygon. In addition, it discusses how to determine the type of polygon given the number of diagonals as well as the sum of the interior angles of a polygon and the measure of each interior angle and exterior angle.
Polygons:
https://www.youtube.com/watch?v=E_-3ulbtcLk
Angles of Regular Polygons:
https://www.youtube.com/watch?v=OEzEo4XqzJQ
Quadrilaterals:
https://www.youtube.com/watch?v=ogcH3eM5beM
Parallelograms: ...
published: 27 Dec 2017
Polygonal Numbers Pentagonal
Video Tutorial For Finding the Terms of Polygonal Numbers (Pentagonal)
published: 19 Jan 2019
How to find a Term of any Polygonal number sequence ? #maths #tricks #polygonal
FORMULA :
[(p - 2)n - (p - 4)]n/2
published: 03 Nov 2024
Adding Polygonal Numbers
http://demonstrations.wolfram.com/AddingPolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A polygonal number is a natural number p such that p dots can be arrranged in an array shaped like a regular triangle, square, etc. In general, any n -gonal number is equal to the sum of the (n - 1) -gonal number of the same rank and the triangular numb...
Contributed by: Enrique Zeleny
Based on a program by: Eric W. Weisstein
Derivation of Formula to find nth polygonal number. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtube.c...
Derivation of Formula to find nth polygonal number. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtube.com/MathsSmart
Derivation of Formula to find nth polygonal number. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtube.com/MathsSmart
Learn about polygonal Numbers a topic of Number Theory. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtu...
Learn about polygonal Numbers a topic of Number Theory. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtube.com/MathsSmart
Learn about polygonal Numbers a topic of Number Theory. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtube.com/MathsSmart
http://demonstrations.wolfram.com/PolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries ...
http://demonstrations.wolfram.com/PolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., numbers to an n -gon for arbitrary positive integer n. The diagram graphically illustrates the process by which the k th n -gonal number is generated.
Contributed by: Eric W. Weisstein
http://demonstrations.wolfram.com/PolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., numbers to an n -gon for arbitrary positive integer n. The diagram graphically illustrates the process by which the k th n -gonal number is generated.
Contributed by: Eric W. Weisstein
This playlist contains proofs without words and visualizations of various figurate numbers and relationships among figurate numbers. Polygonal numbers (e.g., tr...
This playlist contains proofs without words and visualizations of various figurate numbers and relationships among figurate numbers. Polygonal numbers (e.g., triangular, square, pentagonal, hexagonal, heptagonal, octagonal numbers) and centered polygonal numbers (e.g., hex numbers) along with other types of figurate numbers (e.g., star numbers) are also considered.
This playlist contains proofs without words and visualizations of various figurate numbers and relationships among figurate numbers. Polygonal numbers (e.g., triangular, square, pentagonal, hexagonal, heptagonal, octagonal numbers) and centered polygonal numbers (e.g., hex numbers) along with other types of figurate numbers (e.g., star numbers) are also considered.
This geometry video tutorial explains how to calculate the number of diagonals in a regular polygon such as a square, pentagon, hexagon, heptagon, and an octago...
This geometry video tutorial explains how to calculate the number of diagonals in a regular polygon such as a square, pentagon, hexagon, heptagon, and an octagon. It also explains how to confirm the answer by drawing the diagonals in a regular polygon. In addition, it discusses how to determine the type of polygon given the number of diagonals as well as the sum of the interior angles of a polygon and the measure of each interior angle and exterior angle.
Polygons:
https://www.youtube.com/watch?v=E_-3ulbtcLk
Angles of Regular Polygons:
https://www.youtube.com/watch?v=OEzEo4XqzJQ
Quadrilaterals:
https://www.youtube.com/watch?v=ogcH3eM5beM
Parallelograms:
https://www.youtube.com/watch?v=t42sLuns4Qs
Rectangles - Special Quadrilaterals:
https://www.youtube.com/watch?v=Ov4aTty67A8
Isosceles Trapezoids:
https://www.youtube.com/watch?v=AlyWS8bG3kE
_________________________________
The Rhombus:
https://www.youtube.com/watch?v=uXo_Vpctmrg
Kites:
https://www.youtube.com/watch?v=UTgF6lSAMa8
Proving Parallelograms:
https://www.youtube.com/watch?v=MQJnPfNb2Og
Proving a Quadrilateral Is a Kite:
https://www.youtube.com/watch?v=dh8vRzTNVBg
Proving a Quadrilateral Is a Rhombus:
https://www.youtube.com/watch?v=EtoP5G98sok
__________________________________
Proving Isosceles Trapezoids:
https://www.youtube.com/watch?v=EvTHRcNBAc8
2 Column Proofs - Quadrilateral:
https://www.youtube.com/watch?v=m8BlpR7xhiM
Skew Lines:
https://www.youtube.com/watch?v=cemF45vNOhg
Points, Lines, Planes, & Segments:
https://www.youtube.com/watch?v=dDWjhRfBsKM
_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
This geometry video tutorial explains how to calculate the number of diagonals in a regular polygon such as a square, pentagon, hexagon, heptagon, and an octagon. It also explains how to confirm the answer by drawing the diagonals in a regular polygon. In addition, it discusses how to determine the type of polygon given the number of diagonals as well as the sum of the interior angles of a polygon and the measure of each interior angle and exterior angle.
Polygons:
https://www.youtube.com/watch?v=E_-3ulbtcLk
Angles of Regular Polygons:
https://www.youtube.com/watch?v=OEzEo4XqzJQ
Quadrilaterals:
https://www.youtube.com/watch?v=ogcH3eM5beM
Parallelograms:
https://www.youtube.com/watch?v=t42sLuns4Qs
Rectangles - Special Quadrilaterals:
https://www.youtube.com/watch?v=Ov4aTty67A8
Isosceles Trapezoids:
https://www.youtube.com/watch?v=AlyWS8bG3kE
_________________________________
The Rhombus:
https://www.youtube.com/watch?v=uXo_Vpctmrg
Kites:
https://www.youtube.com/watch?v=UTgF6lSAMa8
Proving Parallelograms:
https://www.youtube.com/watch?v=MQJnPfNb2Og
Proving a Quadrilateral Is a Kite:
https://www.youtube.com/watch?v=dh8vRzTNVBg
Proving a Quadrilateral Is a Rhombus:
https://www.youtube.com/watch?v=EtoP5G98sok
__________________________________
Proving Isosceles Trapezoids:
https://www.youtube.com/watch?v=EvTHRcNBAc8
2 Column Proofs - Quadrilateral:
https://www.youtube.com/watch?v=m8BlpR7xhiM
Skew Lines:
https://www.youtube.com/watch?v=cemF45vNOhg
Points, Lines, Planes, & Segments:
https://www.youtube.com/watch?v=dDWjhRfBsKM
_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
http://demonstrations.wolfram.com/AddingPolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new ...
http://demonstrations.wolfram.com/AddingPolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A polygonal number is a natural number p such that p dots can be arrranged in an array shaped like a regular triangle, square, etc. In general, any n -gonal number is equal to the sum of the (n - 1) -gonal number of the same rank and the triangular numb...
Contributed by: Enrique Zeleny
Based on a program by: Eric W. Weisstein
http://demonstrations.wolfram.com/AddingPolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A polygonal number is a natural number p such that p dots can be arrranged in an array shaped like a regular triangle, square, etc. In general, any n -gonal number is equal to the sum of the (n - 1) -gonal number of the same rank and the triangular numb...
Contributed by: Enrique Zeleny
Based on a program by: Eric W. Weisstein
Derivation of Formula to find nth polygonal number. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtube.com/MathsSmart
Learn about polygonal Numbers a topic of Number Theory. For more videos on this topic and many more interesting topics visit or subscribe to : https://www.youtube.com/MathsSmart
http://demonstrations.wolfram.com/PolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., numbers to an n -gon for arbitrary positive integer n. The diagram graphically illustrates the process by which the k th n -gonal number is generated.
Contributed by: Eric W. Weisstein
This playlist contains proofs without words and visualizations of various figurate numbers and relationships among figurate numbers. Polygonal numbers (e.g., triangular, square, pentagonal, hexagonal, heptagonal, octagonal numbers) and centered polygonal numbers (e.g., hex numbers) along with other types of figurate numbers (e.g., star numbers) are also considered.
This geometry video tutorial explains how to calculate the number of diagonals in a regular polygon such as a square, pentagon, hexagon, heptagon, and an octagon. It also explains how to confirm the answer by drawing the diagonals in a regular polygon. In addition, it discusses how to determine the type of polygon given the number of diagonals as well as the sum of the interior angles of a polygon and the measure of each interior angle and exterior angle.
Polygons:
https://www.youtube.com/watch?v=E_-3ulbtcLk
Angles of Regular Polygons:
https://www.youtube.com/watch?v=OEzEo4XqzJQ
Quadrilaterals:
https://www.youtube.com/watch?v=ogcH3eM5beM
Parallelograms:
https://www.youtube.com/watch?v=t42sLuns4Qs
Rectangles - Special Quadrilaterals:
https://www.youtube.com/watch?v=Ov4aTty67A8
Isosceles Trapezoids:
https://www.youtube.com/watch?v=AlyWS8bG3kE
_________________________________
The Rhombus:
https://www.youtube.com/watch?v=uXo_Vpctmrg
Kites:
https://www.youtube.com/watch?v=UTgF6lSAMa8
Proving Parallelograms:
https://www.youtube.com/watch?v=MQJnPfNb2Og
Proving a Quadrilateral Is a Kite:
https://www.youtube.com/watch?v=dh8vRzTNVBg
Proving a Quadrilateral Is a Rhombus:
https://www.youtube.com/watch?v=EtoP5G98sok
__________________________________
Proving Isosceles Trapezoids:
https://www.youtube.com/watch?v=EvTHRcNBAc8
2 Column Proofs - Quadrilateral:
https://www.youtube.com/watch?v=m8BlpR7xhiM
Skew Lines:
https://www.youtube.com/watch?v=cemF45vNOhg
Points, Lines, Planes, & Segments:
https://www.youtube.com/watch?v=dDWjhRfBsKM
_______________________________________
Final Exams and Video Playlists:
https://www.video-tutor.net/
Full-Length Videos and Worksheets:
https://www.patreon.com/MathScienceTutor/collections
http://demonstrations.wolfram.com/AddingPolygonalNumbers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A polygonal number is a natural number p such that p dots can be arrranged in an array shaped like a regular triangle, square, etc. In general, any n -gonal number is equal to the sum of the (n - 1) -gonal number of the same rank and the triangular numb...
Contributed by: Enrique Zeleny
Based on a program by: Eric W. Weisstein
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.
But 10 cannot be arranged as a square. The number 9, on the other hand, can be (see square number):
Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number):
By convention, 1 is the first polygonal number for any number of sides. The rule for enlarging the polygon to the next size is to extend two adjacent arms by one point and to then add the required extra sides between those points. In the following diagrams, each extra layer is shown as in red.
Triangular numbers
Square numbers
Polygons with higher numbers of sides, such as pentagons and hexagons, can also be constructed according to this rule, although the dots will no longer form a perfectly regular lattice like above.
And one need only look to the games industry to see why—despite $184 billion in sales, there were over 10,000 layoffs in 2023, according to Polygon. It's numbers like that that make clear the issue ...
And one need only look to the games industry to see why—despite $184 billion in sales, there were over 10,000 layoffs in 2023, according to Polygon. It’s numbers like that that make clear the issue ...
... in numbers ... The total number of polygons impacted is massive - over 1 crore (10012716) covering 92,989.39 km2 and a major cause of concerns,” said Chetan Agarwal, a Gurugram-based forest analyst.
Puzzles ... Crossword. Polygon. Sudoku. Age is but a number and we all know that good genes, a healthy diet and the right type and amount of exercise can leave us physically better off than our birth date implies ... HEALTH ... .
The biggest benefit of this upgrade is the ability to use your existing Polygon account (via the email address that’s tied to it) across a number of Vox Media sites! For now, this functionality ...
Image. EA ...SplitFiction ... Polygon did a deep dive into the game’s sales numbers, determining that it sold at an astonishingly consistent and enviable clip of half a million copies per month since its release in March 2021 ... Warzone and Fortnite ... .
SuccessfulPolygon (POL) switch interests broader market. Since Polygon made a 1.1... Polygon’s PoS blockchain also posted impressive numbers on the weekly chart, recording net flows of almost $10 million.
It breaks down compliance metrics, such as Deforested Status, Land Approved for Farming, Spatial Legality Violations, and Compliance Status, from producers to individual polygon numbers ... polygon data.
In this article, we’ll look closely at Cardano (ADA), Polygon (POL), Solana (SOL), and Minotaurus (MTAUR) ...Beyond the numbers, MTAUR powers incredible in-game features ... Cardano’s numbers show strong growth ... The numbers show Polygon is building strength.
If it were up to me, Balatro would be numbers 1-50, but apparently not everyone agrees and this is perhaps why I was not invited to join Polygon’s decision committee this year.
Polygon, known for its focus on Ethereum compatibility and scalability, also attracts a large number of decentralized applications, thanks to its low fees and fast transaction speeds.
Photo. Stormy Pyeatte for The Verge. Lila was created from the limited options available. female, blue hair, face “number two.” She was there on the next screen, pastel and polygonal, bobbing slightly as she stood in a bare apartment ... .
Publisher Playstack wasn’t able to comment on sales numbers, but told Polygon via email that Balatro’s daily active players are seeing a “significant spike” since the news broke.