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geometry

  

RegularStarPolygon

  

define a regular star polygon

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RegularStarPolygon(p, n, cen, rad )

Parameters

p

-

the name of the regular star polygon

n

-

positive rational number > 2

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

• 

Let S be a rotation through angle 2πn, and let A_0 be any point not on the axis of S. Then the points Ai=A0Si,i=...,2,1,0,1,2,... are the vertices of a regular polygon n whose sides are the segments A_0A_1, A_1A_2, ...

• 

When n is an integer (greater than 2) this definition is equivalent to that given for regular polyhedra. But the polygon can be closed without n being integral; it is merely necessary that the period of S to be finite, i.e., that n be rational. We still stipulate that 2<n since a positive rotation through an angle greater than Pi is the same as a negative rotation through an angle less than Pi.

• 

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

form(p)

returns the form of the geometric object

 

(i.e., RegularStarPolygon2d 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.

InteriorAngle(p)

returns the interior angle of p.

ExteriorAngle(p)

returns the exterior angle 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,RegularStarPolygon) allows the use of the abbreviated form of this command.

Examples

withgeometry&colon;

RegularStarPolygongon&comma;52&comma;pointo&comma;0&comma;0&comma;1

gon

(1)

detailgon

name of the objectgonform of the objectRegularStarPolygon2dthe side of the polygon2csc2π5the center of the polygon0&comma;0the radius of the circum-circle1the interior angleπ5the exterior angle4π5the perimeter10csc2π5the area5sin2π5cos2π52the vertices of the polygon1&comma;0&comma;cosπ5&comma;sinπ5&comma;cos2π5&comma;sin2π5&comma;cos2π5&comma;sin2π5&comma;cosπ5&comma;sinπ5

(2)

See Also

geometry[RegularPolygon]

 


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