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RegularPolygon

  

define a regular polygon

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RegularPolygon(p, n, cen, rad)

Parameters

p

-

the name of the regular polygon

n

-

positive integer >= 3

cen

-

point which is the center of the n-gon

rad

-

number which is the radius of the circumscribed circle of the n-gon

Description

• 

A p-gon is regular if it is both equilateral and equiangular.

• 

A regular polygon is easily seen to have a center, from which all the vertices are at the same distance R0, while all the sides are at the same distance R1. This means that there are two concentric circles, the circum-circle and the in-circle, which pass through the vertices and touch the sides, respectively.

• 

To access the information relating to a regular polygon p, use the following function calls:

form(p)

returns the form of the geometric object

 

(i.e., RegularPolygon2d if p is a regular polygon).

DefinedAs(p)

returns a list of vertices of p.

sides(p)

returns the side of p.

center(p)

returns the center of p.

radius(p)

returns the radius of the circum-circle of p.

inradius(p)

returns the radius of the in-circle of p.

InteriorAngle(p)

returns the interior angle of p.

ExteriorAngle(p)

returns the exterior angle of p.

apothem(p)

returns the apothem of p.

perimeter(p)

returns the perimeter of p.

area(p)

returns the area of p.

detail(p)

returns a detailed description of the

 

given regular polygon p.

• 

The command with(geometry,RegularPolygon) allows the use of the abbreviated form of this command.

Examples

withgeometry:

RegularPolygongon,5,pointo,1,1,2

gon

(1)

detailgon

name of the objectgonform of the objectRegularPolygon2dthe side of the polygon4sinπ5the center of the polygon1,1the radius of the circum-circle2the radius of the in-circle2cosπ5the interior angle3π5the exterior angle2π5the perimeter20sinπ5the area20sinπ5cosπ5the vertices of the polygon3,1,1+2cos2π5,1+2sin2π5,12cosπ5,1+2sinπ5,12cosπ5,12sinπ5,1+2cos2π5,12sin2π5

(2)

See Also

geometry[RegularStarPolygon]

 


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