Polygonal Numbers
Polygonal numbers are a type of figurate numbers. They generalize triangular numbers, square numbers, etc. to any -gon.
Return the first 10 triangular numbers.
In[1]:=
![Click for copyable input](assets.en/polygonal-numbers/In_7.png)
Table[PolygonalNumber[n], {n, 1, 10}]
Out[1]=
![](assets.en/polygonal-numbers/O_6.png)
Return the tenth -gonal number of several regular polygons.
In[2]:=
![Click for copyable input](assets.en/polygonal-numbers/In_8.png)
Table[PolygonalNumber[r, 10], {r, 3, 10}]
Out[2]=
![](assets.en/polygonal-numbers/O_7.png)
A polygonal number counts the number of equally spaced points in a regular geometrical arrangement of this type.
show complete Wolfram Language input
In[5]:=
![Click for copyable input](assets.en/polygonal-numbers/In_11.png)
PolygonalNumber[3, 4]
polygonalNumberGraphics[3, 4]
Out[5]=
![](assets.en/polygonal-numbers/O_8.png)
Out[5]=
![](assets.en/polygonal-numbers/O_9.png)
In[6]:=
![Click for copyable input](assets.en/polygonal-numbers/In_12.png)
PolygonalNumber[3, 6]
polygonalNumberGraphics[3, 6]
Out[6]=
![](assets.en/polygonal-numbers/O_10.png)
Out[6]=
![](assets.en/polygonal-numbers/O_11.png)
In[7]:=
![Click for copyable input](assets.en/polygonal-numbers/In_13.png)
PolygonalNumber[6, 5]
polygonalNumberGraphics[6, 5]
Out[7]=
![](assets.en/polygonal-numbers/O_12.png)
Out[7]=
![](assets.en/polygonal-numbers/O_13.png)