# Pentagram

Pentagram
You are encouraged to solve this task according to the task description, using any language you may know.

A pentagram is a star polygon, consisting of a central pentagon of which each side forms the base of an isosceles triangle. The vertex of each triangle, a point of the star, is 36 degrees.

Draw (or print) a regular pentagram, in any orientation. Use a different color (or token) for stroke and fill, and background. For the fill it should be assumed that all points inside the triangles and the pentagon are inside the pentagram.

## Action!

```INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit

DEFINE REALPTR="CARD"
TYPE PointR=[REALPTR x,y]

INT ARRAY SinTab=[
0 4 9 13 18 22 27 31 36 40 44 49 53 58 62 66 71 75 79 83
88 92 96 100 104 108 112 116 120 124 128 132 136 139 143
147 150 154 158 161 165 168 171 175 178 181 184 187 190
193 196 199 202 204 207 210 212 215 217 219 222 224 226
228 230 232 234 236 237 239 241 242 243 245 246 247 248
249 250 251 252 253 254 254 255 255 255 256 256 256 256]

INT FUNC Sin(INT a)
WHILE a<0 DO a==+360 OD
WHILE a>360 DO a==-360 OD
IF a<=90 THEN
RETURN (SinTab(a))
ELSEIF a<=180 THEN
RETURN (SinTab(180-a))
ELSEIF a<=270 THEN
RETURN (-SinTab(a-180))
ELSE
RETURN (-SinTab(360-a))
FI
RETURN (0)

INT FUNC Cos(INT a)
RETURN (Sin(a-90))

PROC Det(REAL POINTER x1,y1,x2,y2,res)
REAL tmp1,tmp2

RealMult(x1,y2,tmp1)
RealMult(y1,x2,tmp2)
RealSub(tmp1,tmp2,res)
RETURN

BYTE FUNC IsZero(REAL POINTER a)
CHAR ARRAY s(10)

StrR(a,s)
IF s(0)=1 AND s(1)='0 THEN
RETURN (1)
FI
RETURN (0)

BYTE FUNC Intersection(PointR POINTER p1,p2,p3,p4,res)
REAL det1,det2,dx1,dx2,dy1,dy2,nom,denom

Det(p1.x,p1.y,p2.x,p2.y,det1)
Det(p3.x,p3.y,p4.x,p4.y,det2)
RealSub(p1.x,p2.x,dx1)
RealSub(p1.y,p2.y,dy1)
RealSub(p3.x,p4.x,dx2)
RealSub(p3.y,p4.y,dy2)
Det(dx1,dy1,dx2,dy2,denom)

IF IsZero(denom) THEN
RETURN (0)
FI

Det(det1,dx1,det2,dx2,nom)
RealDiv(nom,denom,res.x)
Det(det1,dy1,det2,dy2,nom)
RealDiv(nom,denom,res.y)
RETURN (1)

PROC FloodFill(BYTE x0,y0)
BYTE ARRAY xs(300),ys(300)
INT first,last

first=0 last=0
xs(first)=x0
ys(first)=y0

WHILE first<=last
DO
x0=xs(first) y0=ys(first)
first==+1
IF Locate(x0,y0)=0 THEN
Plot(x0,y0)
IF Locate(x0-1,y0)=0 THEN
last==+1 xs(last)=x0-1 ys(last)=y0
FI
IF Locate(x0+1,y0)=0 THEN
last==+1 xs(last)=x0+1 ys(last)=y0
FI
IF Locate(x0,y0-1)=0 THEN
last==+1 xs(last)=x0 ys(last)=y0-1
FI
IF Locate(x0,y0+1)=0 THEN
last==+1 xs(last)=x0 ys(last)=y0+1
FI
FI
OD
RETURN

PROC Pentagram(INT x0,y0,r,a0 BYTE c1,c2)
INT ARRAY xs(16),ys(16)
INT angle
BYTE i
PointR p1,p2,p3,p4,p
REAL p1x,p1y,p2x,p2y,p3x,p3y,p4x,p4y,px,py

p1.x=p1x p1.y=p1y
p2.x=p2x p2.y=p2y
p3.x=p3x p3.y=p3y
p4.x=p4x p4.y=p4y
p.x=px p.y=py

;outer points
angle=a0
FOR i=0 TO 4
DO
xs(i)=r*Sin(angle)/256+x0
ys(i)=r*Cos(angle)/256+y0
angle==+144
OD

;intersection points
FOR i=0 TO 4
DO
IntToReal(xs(i MOD 5),p1x)
IntToReal(ys(i MOD 5),p1y)
IntToReal(xs((1+i) MOD 5),p2x)
IntToReal(ys((1+i) MOD 5),p2y)
IntToReal(xs((2+i) MOD 5),p3x)
IntToReal(ys((2+i) MOD 5),p3y)
IntToReal(xs((3+i) MOD 5),p4x)
IntToReal(ys((3+i) MOD 5),p4y)
Intersection(p1,p2,p3,p4,p)
xs(5+i)=RealToInt(px)
ys(5+i)=RealToInt(py)
OD

;centers of triangles
FOR i=0 TO 4
DO
xs(10+i)=(xs(i)+xs(5+i)+xs(5+(i+2) MOD 5))/3
ys(10+i)=(ys(i)+ys(5+i)+ys(5+(i+2) MOD 5))/3
OD

;center of pentagon
xs(15)=0 ys(15)=0
FOR i=5 TO 9
DO
xs(15)==+xs(i)
ys(15)==+ys(i)
OD
xs(15)==/5 ys(15)==/5

;draw lines
COLOR=c1
FOR i=0 TO 5
DO
IF i=0 THEN
Plot(xs(i MOD 5),ys(i MOD 5))
ELSE
DrawTo(xs(i MOD 5),ys(i MOD 5))
FI
OD

;fill
COLOR=c2
FOR i=10 TO 15
DO
FloodFill(xs(i),ys(i))
OD
RETURN

PROC Main()
BYTE CH=\$02FC

Graphics(7+16)
SetColor(0,8,4)
SetColor(1,8,8)
SetColor(2,8,12)
Pentagram(40,48,40,0,1,2)
Pentagram(119,48,40,15,2,3)

DO UNTIL CH#\$FF OD
CH=\$FF
RETURN```
Output:

```with Ada.Numerics.Elementary_Functions;

with SDL.Video.Windows.Makers;
with SDL.Video.Renderers.Makers;
with SDL.Video.Rectangles;
with SDL.Events.Events;

procedure Pentagram is

Width  : constant := 600;
Height : constant := 600;
Offset : constant := 300.0;

use SDL.Video.Rectangles;
use SDL.C;

Window   : SDL.Video.Windows.Window;
Renderer : SDL.Video.Renderers.Renderer;
Event    : SDL.Events.Events.Events;

type Node_Id is mod 5;
Nodes : array (Node_Id) of Point;

procedure Calculate is
begin
for I in Nodes'Range loop
Nodes (I) := (X => int (Offset + Radius * Sin (Float (I), Cycle => 5.0)),
Y => int (Offset - Radius * Cos (Float (I), Cycle => 5.0)));
end loop;
end Calculate;

function Orient_2D (A, B, C : Point) return int is
((B.X - A.X) * (C.Y - A.Y) - (B.Y - A.Y) * (C.X - A.X));

procedure Fill is
Count : Natural;
begin
for Y in int (Offset - Radius) .. int (Offset + Radius) loop
for X in int (Offset - Radius) .. int (Offset + Radius) loop
Count := 0;
for Node in Nodes'Range loop
Count := Count +
(if Orient_2D (Nodes (Node), Nodes (Node + 2), (X, Y)) > 0 then 1 else 0);
end loop;
if Count in 4 .. 5 then
Renderer.Draw (Point => (X, Y));
end if;
end loop;
end loop;
end Fill;

procedure Draw_Outline is
begin
for Node in Nodes'Range loop
Renderer.Draw (Line => (Nodes (Node), Nodes (Node + 2)));
end loop;
end Draw_Outline;

procedure Wait is
use type SDL.Events.Event_Types;
begin
loop
SDL.Events.Events.Wait (Event);
exit when Event.Common.Event_Type = SDL.Events.Quit;
end loop;
end Wait;

begin
if not SDL.Initialise (Flags => SDL.Enable_Screen) then
return;
end if;

SDL.Video.Windows.Makers.Create (Win      => Window,
Title    => "Pentagram",
Position => SDL.Natural_Coordinates'(X => 10, Y => 10),
Size     => SDL.Positive_Sizes'(Width, Height),
Flags    => 0);
SDL.Video.Renderers.Makers.Create (Renderer, Window.Get_Surface);
Renderer.Set_Draw_Colour ((0, 0, 0, 255));
Renderer.Fill (Rectangle => (0, 0, Width, Height));

Calculate;
Renderer.Set_Draw_Colour ((50, 50, 150, 255));
Fill;
Renderer.Set_Draw_Colour ((0, 220, 0, 255));
Draw_Outline;
Window.Update_Surface;

Wait;
Window.Finalize;
SDL.Finalise;
end Pentagram;
```

## AutoHotkey

```#Include Gdip.ahk	; https://autohotkey.com/boards/viewtopic.php?f=6&t=6517
Width :=A_ScreenWidth, Height := A_ScreenHeight
Gui, 1: +E0x20 +Caption +E0x80000 +LastFound +AlwaysOnTop +ToolWindow +OwnDialogs
Gui, 1: Show, NA
hwnd1 := WinExist()
OnExit, Exit

If !pToken := Gdip_Startup()
{
MsgBox, 48, gdiplus error!, Gdiplus failed to start.
ExitApp
}

hbm := CreateDIBSection(Width, Height)
hdc := CreateCompatibleDC()
obm := SelectObject(hdc, hbm)
G := Gdip_GraphicsFromHDC(hdc)
Gdip_SetSmoothingMode(G, 4)
pBrush 	:= Gdip_BrushCreateSolid(0xFF6495ED)
pPen 	:= Gdip_CreatePen(0xff000000, 3)

;---------------------------------
LL := 165
Cx := Floor(A_ScreenWidth/2)
Cy := Floor(A_ScreenHeight/2)
phi := 54
;---------------------------------
loop, 5
{
theta := abs(180-144-phi)
p1x := Floor(Cx + LL * Cos(phi * 0.01745329252))
p1y := Floor(Cy + LL * Sin(phi * 0.01745329252))
p2x := Floor(Cx - LL * Cos(theta * 0.01745329252))
p2y := Floor(Cy - LL * Sin(theta * 0.01745329252))
phi+= 72
Gdip_FillPolygon(G, pBrush, p1x "," p1y "|" Cx "," Cy "|" p2x "," p2y)
}
loop, 5
{
theta := abs(180-144-phi)
p1x := Floor(Cx + LL * Cos(phi * 0.01745329252))
p1y := Floor(Cy + LL * Sin(phi * 0.01745329252))
p2x := Floor(Cx - LL * Cos(theta * 0.01745329252))
p2y := Floor(Cy - LL * Sin(theta * 0.01745329252))
phi+= 72
Gdip_DrawLines(G, pPen, p1x "," p1y "|" p2x "," p2y ) ; "|" Cx "," Cy )
}
UpdateLayeredWindow(hwnd1, hdc, 0, 0, Width, Height)
Gdip_DeleteBrush(pBrush)
SelectObject(hdc, obm)
DeleteObject(hbm)
DeleteDC(hdc)
Gdip_DeleteGraphics(G)
return
;----------------------------------------------------------------------
Esc::
Exit:
Gdip_Shutdown(pToken)
ExitApp
Return
```

## BASIC

### Applesoft BASIC

```100 XO = 140
110 YO = 96
120 S = 90
130 B = 7
140 F = 6
150 C = 4
200 POKE 230,64
210 HCOLOR= B
220 HPLOT 0,0
230 CALL 62454
240 A = 49232
250 I =  PEEK (A + 7) +  PEEK (A + 2)
260 I =  PEEK (A + 5) +  PEEK (A)
300 SX = S
310 SY = S
320 PI = 3.1415926535
330 E = PI * 4
340 S = PI / 1.25
350 X =  SIN (0)
360 Y =  COS (0)
370 HCOLOR= F
380 PX = XO + X * SX
390 PY = YO - Y * SY
400 FOR I = 0 TO E STEP S
410     X =  SIN (I)
420     Y =  COS (I)
430     FOR J = 0 TO SX
440         HPLOT PX,PY TO XO + X * J,YO - Y * J
450     NEXT J
460     PX = XO + X * SX
470     PY = YO - Y * SY
480 NEXT I
500 HCOLOR= C
510 PX = XO + X * SX
520 PY = YO - Y * SY
600 FOR I = S TO E STEP S
610     X =  SIN (I)
620     Y =  COS (I)
630     HPLOT PX,PY TO XO + X * SX,YO - Y * SY
640     HPLOT PX + 1,PY TO XO + X * SX + 1,YO - Y * SY
650     HPLOT PX,PY + 1 TO XO + X * SX,YO - Y * SY + 1
660     HPLOT PX + 1,PY + 1 TO XO + X * SX + 1,YO - Y * SY + 1
670     PX = XO + X * SX
680     PY = YO - Y * SY
690 NEXT I
```

### IS-BASIC

```100 PROGRAM "Pentagra.bas"
110 OPTION ANGLE DEGREES
120 GRAPHICS HIRES 4
130 SET PALETTE BLUE,CYAN,YELLOW,BLACK
140 PLOT 640,700,ANGLE 288;
150 FOR I=1 TO 5
160   PLOT FORWARD 700,RIGHT 144;
170 NEXT
180 SET INK 3
190 SET BEAM OFF:PLOT 0,0,PAINT```

### VBA

```Sub pentagram()
With ActiveSheet.Shapes.AddShape(msoShape5pointStar, 10, 10, 400, 400)
.Fill.ForeColor.RGB = RGB(255, 0, 0)
.Line.Weight = 3
.Line.ForeColor.RGB = RGB(0, 0, 255)
End With
End Sub
```

## C

Interactive program which takes the side lengths of the pentagram's core, it's arms and the colours for filling the background, drawing the figure and then filling it in. Requires the WinBGIm library.

```#include<graphics.h>
#include<stdio.h>
#include<math.h>

#define pi M_PI

int main(){

char colourNames[][14] = { "BLACK", "BLUE", "GREEN", "CYAN", "RED", "MAGENTA", "BROWN", "LIGHTGRAY", "DARKGRAY",
"LIGHTBLUE", "LIGHTGREEN", "LIGHTCYAN", "LIGHTRED", "LIGHTMAGENTA", "YELLOW", "WHITE" };

int stroke=0,fill=0,back=0,i;

double centerX = 300,centerY = 300,coreSide,armLength,pentaLength;

printf("Enter core pentagon side length : ");
scanf("%lf",&coreSide);

printf("Enter pentagram arm length : ");
scanf("%lf",&armLength);

printf("Available colours are :\n");

for(i=0;i<16;i++){
printf("%d. %s\t",i+1,colourNames[i]);
if((i+1) % 3 == 0){
printf("\n");
}
}

while(stroke==fill && fill==back){
printf("\nEnter three diffrenet options for stroke, fill and background : ");
scanf("%d%d%d",&stroke,&fill,&back);
}

pentaLength = coreSide/(2 * tan(pi/5)) + sqrt(armLength*armLength - coreSide*coreSide/4);

initwindow(2*centerX,2*centerY,"Pentagram");

setcolor(stroke-1);

setfillstyle(SOLID_FILL,back-1);

bar(0,0,2*centerX,2*centerY);

floodfill(centerX,centerY,back-1);

setfillstyle(SOLID_FILL,fill-1);

for(i=0;i<5;i++){
line(centerX + coreSide*cos(i*2*pi/5)/(2*sin(pi/5)),centerY + coreSide*sin(i*2*pi/5)/(2*sin(pi/5)),centerX + coreSide*cos((i+1)*2*pi/5)/(2*sin(pi/5)),centerY + coreSide*sin((i+1)*2*pi/5)/(2*sin(pi/5)));
line(centerX + coreSide*cos(i*2*pi/5)/(2*sin(pi/5)),centerY + coreSide*sin(i*2*pi/5)/(2*sin(pi/5)),centerX + pentaLength*cos(i*2*pi/5 + pi/5),centerY + pentaLength*sin(i*2*pi/5 + pi/5));
line(centerX + coreSide*cos((i+1)*2*pi/5)/(2*sin(pi/5)),centerY + coreSide*sin((i+1)*2*pi/5)/(2*sin(pi/5)),centerX + pentaLength*cos(i*2*pi/5 + pi/5),centerY + pentaLength*sin(i*2*pi/5 + pi/5));

floodfill(centerX + coreSide*cos(i*2*pi/5 + pi/10)/(2*sin(pi/5)),centerY + coreSide*sin(i*2*pi/5 + pi/10)/(2*sin(pi/5)),stroke-1);
}

floodfill(centerX,centerY,stroke-1);

getch();

closegraph();
}
```

## Delphi

Library: Vcl.Forms
Library: System.Math
```unit Main;

interface

uses
Winapi.Windows, Vcl.Graphics, Vcl.Forms, System.Math;

type
TForm1 = class(TForm)
procedure FormCreate(Sender: TObject);
procedure FormPaint(Sender: TObject);
private
procedure DrawPentagram(len, x, y: Integer; fill, stoke: TColor);
{ Private declarations }
public
{ Public declarations }
end;

var
Form1: TForm1;
degrees144: double;
degrees72: double;
degrees18: double;

implementation

{\$R *.dfm}

procedure TForm1.FormCreate(Sender: TObject);
begin
ClientHeight := 640;
ClientWidth := 640;
end;

procedure CreatePolygon(len, x, y, n: integer; ang: double; var points: TArray<TPoint>);
var
angle: Double;
index, i, x2, y2: Integer;
begin
angle := 0;
index := 0;
SetLength(points, n + 1);
points[index].Create(x, y);

for i := 1 to n do
begin
x2 := x + round(len * cos(angle));
y2 := y + round(len * sin(-angle));
x := x2;
y := y2;
angle := angle - ang;

points[index].Create(x2, y2);
inc(index);
end;
points[index].Create(points[0]);
end;

procedure TForm1.DrawPentagram(len, x, y: Integer; fill, stoke: TColor);
var
points, points_internal: TArray<TPoint>;
L, H: Integer;
begin
// Calc of sides for draw internal pollygon
// 2H+L = len -> 2H = len - L
// L = 2H*sin(36/2) (Pythagorean theorem)
// L = (len-L)sin(18)
// L = len*sin(18)/[1+sin(18)]

L := round(len * sin(degrees18) / (1 + sin(degrees18)));

// H = (len - L)/2

H := (len - L) div 2;

CreatePolygon(L, x + H, y, 5, degrees72, points_internal);
CreatePolygon(len, x, y, 5, degrees144, points);

with Canvas, Canvas.Brush do
begin
with pen do
begin
Color := stoke;
Style := psSolid;
Width := 5;
end;
Color := fill;
Polygon(points_internal);
Polygon(points);
end;
end;

procedure TForm1.FormPaint(Sender: TObject);
begin
with Canvas, Brush do
begin
Style := bsSolid;
Color := clWhite;
// fill background with white
FillRect(ClientRect);
end;
drawPentagram(500, 70, 250, \$ED9564, clDkGray);
end;

end.
```

form code:

```object Form1: TForm1
OnCreate = FormCreate
OnPaint = FormPaint
end
```

## EasyLang

```xp = 10
yp = 60
linewidth 2
move xp yp
while angle < 720
x = xp + cos angle * 80
y = yp + sin -angle * 80
line x y
f[] &= x
f[] &= y
xp = x
yp = y
angle += 144
.
color 900
polygon f[]
```

## Go

Library: Go Graphics
```package main

import (
"github.com/fogleman/gg"
"math"
)

func Pentagram(x, y, r float64) []gg.Point {
points := make([]gg.Point, 5)
for i := 0; i < 5; i++ {
fi := float64(i)
angle := 2*math.Pi*fi/5 - math.Pi/2
points[i] = gg.Point{x + r*math.Cos(angle), y + r*math.Sin(angle)}
}
return points
}

func main() {
points := Pentagram(320, 320, 250)
dc := gg.NewContext(640, 640)
dc.SetRGB(1, 1, 1) // White
dc.Clear()
for i := 0; i <= 5; i++ {
index := (i * 2) % 5
p := points[index]
dc.LineTo(p.X, p.Y)
}
dc.SetHexColor("#6495ED") // Cornflower Blue
dc.SetFillRule(gg.FillRuleWinding)
dc.FillPreserve()
dc.SetRGB(0, 0, 0) // Black
dc.SetLineWidth(5)
dc.Stroke()
dc.SavePNG("pentagram.png")
}
```
Output:
```The image produced is similar to that of the Java entry.
```

This uses the Diagrams library to create an SVG drawing. Compiling, then running it like:

```pentagram -w 400 -o pentagram_hs.svg
```

creates a 400x400 SVG file.

```-- Extract the vertices of a pentagon, re-ordering them so that drawing lines
-- from one to the next forms a pentagram.  Set the line's thickness and its
-- colour, as well as the fill and background colours.  Make the background a
-- bit larger than the pentagram.

import Diagrams.Prelude
import Diagrams.Backend.SVG.CmdLine

pentagram = let [a, b, c, d, e] = trailVertices \$ pentagon 1
in [a, c, e, b, d]
# fromVertices
# closeTrail
# strokeTrail
# lw ultraThick
# fc springgreen
# lc blue
# bgFrame 0.2 bisque

main = mainWith (pentagram :: Diagram B)
```

## J

Probably the simplest approach is:

```require'plot'
plot j./2 1 o./180p_1 %~ 144*i. 6
```

This will give a pentagram with a blue border and a white interior.

## Java

Works with: Java version 8
```import java.awt.*;
import java.awt.geom.Path2D;
import javax.swing.*;

public class Pentagram extends JPanel {

public Pentagram() {
setPreferredSize(new Dimension(640, 640));
setBackground(Color.white);
}

private void drawPentagram(Graphics2D g, int len, int x, int y,
Color fill, Color stroke) {
double angle = 0;

Path2D p = new Path2D.Float();
p.moveTo(x, y);

for (int i = 0; i < 5; i++) {
int x2 = x + (int) (Math.cos(angle) * len);
int y2 = y + (int) (Math.sin(-angle) * len);
p.lineTo(x2, y2);
x = x2;
y = y2;
angle -= degrees144;
}
p.closePath();

g.setColor(fill);
g.fill(p);

g.setColor(stroke);
g.draw(p);
}

@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;

g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);

g.setStroke(new BasicStroke(5, BasicStroke.CAP_ROUND, 0));

drawPentagram(g, 500, 70, 250, new Color(0x6495ED), Color.darkGray);
}

public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Pentagram");
f.setResizable(false);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}
```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

This entry produces SVG output which, if placed in a file with suffix .svg, can be viewed directly in most browsers.

Notice that the size of an appropriate SVG viewBox is computed.

```# Input: {svg, minx, miny, maxx, maxy}
def svg:
# viewBox = <min-x> <min-y> <width> <height>
"<svg viewBox='\(.minx - 4|floor) \(.miny - 4 |floor) \(6 + .maxx - .minx|ceil) \(6 + .maxy - .miny|ceil)'",
"     preserveAspectRatio='xMinYmin meet'",
"     xmlns='http://www.w3.org/2000/svg' >",
.svg,
"</svg>" ;

# Input: an array of [x,y] points
def minmax:
{minx: (map(.[0])|min),
miny: (map(.[1])|min),
maxx: (map(.[0])|max),
maxy: (map(.[1])|max)} ;

# Input: an array of [x,y] points
def Polyline(\$fill; \$stroke; \$transform):
def rnd: 1000*.|round/1000;
def linearize: map( map(rnd) | join(" ") ) | join(", ");

"<polyline points='"
+ linearize
+ "'\n style='fill:\(\$fill); stroke: \(\$stroke); stroke-width:3;'"
+ "\n transform='\(\$transform)' />" ;

# Output: {minx, miny, maxx, maxy, svg}
def pentagram(\$dim):
(8 * (1|atan)) as \$tau
| 5 as \$sides
| [ (0, 2, 4, 1, 3, 0)
| [  0.9 * \$dim * ((\$tau * \$v / \$sides) | cos),
0.9 * \$dim * ((\$tau * \$v / \$sides) | sin) ] ]
| minmax
+ {svg: Polyline("seashell"; "blue"; "rotate(-18)" )} ;

pentagram(200)
| svg```
Output:
```<svg viewBox='-150 -176 332 349'
preserveAspectRatio='xMinYmin meet'
xmlns='http://www.w3.org/2000/svg' >
<polyline points='180 0, -145.623 105.801, 55.623 -171.19, 55.623 171.19, -145.623 -105.801, 180 0'
style='fill:seashell; stroke: blue; stroke-width:3;'
transform='rotate(-18)' />
</svg>
```

## Julia

```using Luxor

function drawpentagram(path::AbstractString, w::Integer=1000, h::Integer=1000)
Drawing(h, w, path)
origin()
setline(16)

# To get a different color border from the fill, draw twice, first with fill, then without.
sethue("aqua")
star(0, 0, 500, 5, 0.39, 3pi/10, :fill)

sethue("navy")
verts = star(0, 0, 500, 5, 0.5, 3pi/10, vertices=true)
poly([verts[i] for i in [1,5,9,3,7,1]], :stroke)
finish()
preview()
end

drawpentagram("data/pentagram.png")
```

## Kotlin

Translation of: Java
```// version 1.1.2

import java.awt.*
import java.awt.geom.Path2D
import javax.swing.*

class Pentagram : JPanel() {
init {
preferredSize = Dimension(640, 640)
background = Color.white
}

private fun drawPentagram(g: Graphics2D, len: Int, x: Int, y: Int,
fill: Color, stroke: Color) {
var x2 = x.toDouble()
var y2 = y.toDouble()
var angle = 0.0
val p = Path2D.Float()
p.moveTo(x2, y2)

for (i in 0..4) {
x2 += Math.cos(angle) * len
y2 += Math.sin(-angle) * len
p.lineTo(x2, y2)
}

p.closePath()
with(g) {
color = fill
fill(p)
color = stroke
draw(p)
}
}

override fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON)
g.stroke = BasicStroke(5.0f, BasicStroke.CAP_ROUND, 0)
drawPentagram(g, 500, 70, 250, Color(0x6495ED), Color.darkGray)
}
}

fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
with(f) {
defaultCloseOperation = JFrame.EXIT_ON_CLOSE
title = "Pentagram"
isResizable = false
pack()
setLocationRelativeTo(null)
isVisible = true
}
}
}
```

## Lua

Using the Bitmap class here, with an ASCII pixel representation, then extending with `line()` as here, then extending with `floodfill()` as here, then extending further..

```local cos, sin, floor, pi = math.cos, math.sin, math.floor, math.pi

function Bitmap:render()
for y = 1, self.height do
print(table.concat(self.pixels[y]))
end
end

function Bitmap:pentagram(x, y, radius, rotation, outlcolor, fillcolor)
local x1, y1 = pxy(0)
for i = 1, 5 do
local x2, y2 = pxy(i*2) -- btw: pxy(i) ==> pentagon
self:line(floor(x1*2), floor(y1), floor(x2*2), floor(y2), outlcolor)
x1, y1 = x2, y2
end
self:floodfill(floor(x*2), floor(y), fillcolor)
for i = 1, 5 do
x1, y1 = pxy(i)
self:floodfill(floor(x1*2), floor(y1), fillcolor)
end
end

bitmap = Bitmap(40*2,40)
bitmap:clear(".")
bitmap:pentagram(20, 22, 20, -pi/2, "@", '+')
bitmap:render()
```
Output:
```................................................................................
................................................................................
.......................................@@.......................................
......................................@++@......................................
......................................@++@......................................
.....................................@++++@.....................................
....................................@++++++@....................................
....................................@++++++@....................................
...................................@++++++++@...................................
...................................@++++++++@...................................
..................................@++++++++++@..................................
.................................@++++++++++++@.................................
.................................@++++++++++++@.................................
................................@++++++++++++++@................................
...............................@++++++++++++++++@...............................
.@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@.
....@@@+++++++++++++++++++++++@++++++++++++++++++@+++++++++++++++++++++++++@@@..
.......@@++++++++++++++++++++@++++++++++++++++++++@++++++++++++++++++++++@@.....
.........@@@+++++++++++++++++@++++++++++++++++++++@+++++++++++++++++++@@@.......
............@@@+++++++++++++@++++++++++++++++++++++@+++++++++++++++@@@..........
...............@@++++++++++@+++++++++++++++++++++++@+++++++++++++@@.............
.................@@@+++++++@++++++++++++++++++++++++@+++++++++@@@...............
....................@@@+++@++++++++++++++++++++++++++@+++++@@@..................
.......................@@+@++++++++++++++++++++++++++@+++@@.....................
.........................@@@++++++++++++++++++++++++++@@@.......................
........................@+++@@@++++++++++++++++++++@@@+@........................
........................@++++++@@+++++++++++++++@@@++++@........................
.......................@+++++++++@@@++++++++++@@++++++++@.......................
......................@+++++++++++++@@@++++@@@+++++++++++@......................
......................@++++++++++++++++@@@@++++++++++++++@......................
.....................@++++++++++++++++@@..@@++++++++++++++@.....................
....................@++++++++++++++@@@......@@@++++++++++++@....................
....................@+++++++++++@@@............@@@+++++++++@....................
...................@++++++++++@@..................@@++++++++@...................
...................@+++++++@@@......................@@@+++++@...................
..................@+++++@@@............................@@@+++@..................
.................@++++@@..................................@@++@.................
.................@+@@@......................................@@@.................
................@@@............................................@................
................................................................................```

## Maple

```with(geometry):
RegularStarPolygon(middle, 5/2, point(c, 0, 0), 1):
v := [seq(coordinates(i), i in DefinedAs(middle))]:
pentagram := plottools[rotate](plottools[polygon](v), Pi/2):
plots[display](pentagram, colour = yellow, axes = none);```
Output:

Note: Plot shown below is generated using interface(plotdevice = char);

```                                       C
C C
C   C
C     C
C       C
CC         CC
C             C
C               C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCC                   C                   C                   CCCC
CCCCC             C                     C             CCCCC
CCCC         C                     C         CCCC
CCCCC   C                       C   CCCCC
CCCC                       CCCC
C  CCCCC             CCCCC  C
C        CCCC     CCCC        C
CC             CCCCC             CC
C           CCCCC   CCCCC           C
C        CCCC             CCCC        C
C    CCCCC                     CCCCC    C
C CCCC                               CCCC C
CCC                                       CCC
```

## Mathematica /Wolfram Language

```Graphics[{
EdgeForm[Directive[Thickness[0.01], RGBColor[0, 0, 1]]],(*Edge coloring*)
RGBColor[0.5, 0.5, .50], (*Fill coloring*)
Polygon[AnglePath[Table[6 Pi/5, 5]]]}
]
```

## Nim

Works with: nim version 1.4.4
Library: nim-libgd
```import libgd
from math import sin, cos, degToRad

const
width = 500
height = width

proc main() =

proc calcPosition(x: int, y: int, radius: int, posAngle: float): (cint, cint) =
return (cast[cint](x + width), cast[cint](y - height))

proc getPentagonPoints(startAngle = 0, radius: int): array[5, array[2, int]] =
let spacingAngle = 360 / 5

var posAngle = (90 - startAngle).float

var n = 0
var points: array[5, array[2, int]]
while n < 5:
(points[n][0], points[n][1]) = calcPosition(250, 250, radius, posAngle)
n += 1
posAngle -= spacingAngle

return points

let outerPentagon = getPentagonPoints(18, outerRadius) # rotate 18 degrees

var pentagram: array[10, array[2, int]]
var n = 0
for i in countup(0, 4):
pentagram[n] = outerPentagon[i]
inc(n)
pentagram[n] = innerPentagon[i]
inc(n)

withGd imageCreate(width, height) as img:

let black = img.setColor(0x404040)
let blue = img.setColor(0x6495ed)

img.drawPolygon(
points=pentagram,
color=blue,
fill=true,
open=false)

img.setThickness(4)

img.drawPolygon(
points=pentagram,
color=black,
fill=false,
open=false)

img.drawPolygon(
points=innerPentagon,
color=black,
fill=false,
open=false)

let png_out = open("pentagram.png", fmWrite)
img.writePng(png_out)

png_out.close()

main()
```

## ooRexx

```/* REXX ***************************************************************
* Create a BMP file showing a pentagram
**********************************************************************/
pentagram='pentagram.bmp'
'erase' pentagram
s='424d4600000000000000360000002800000038000000280000000100180000000000'X
s=s'1000000000000000000000000000000000000000'x
Say 'sl='length(s)
z.0=0
white='ffffff'x
red  ='00ff00'x
green='ff0000'x
blue ='0000ff'x
rd6=copies(rd,6)
m=133
m=80
n=80
hor=m*8      /* 56 */
ver=n*8      /* 40 */
Say 'hor='hor
Say 'ver='ver
Say 'sl='length(s)
s=overlay(lend(hor),s,19,4)
s=overlay(lend(ver),s,23,4)
Say 'sl='length(s)
z.=copies('ffffff'x,3192%3)
z.=copies('ffffff'x,8*m)
z.0=648
s72 =RxCalcsin(72,,'D')
c72 =RxCalccos(72,,'D')
s144=RxCalcsin(144,,'D')
c144=RxCalccos(144,,'D')
xm=300
ym=300
r=200
p.0x.1=xm
p.0y.1=ym+r
p.0x.2=format(xm+r*s72,3,0)
p.0y.2=format(ym+r*c72,3,0)
p.0x.3=format(xm+r*s144,3,0)
p.0y.3=format(ym+r*c144,3,0)
p.0x.4=format(xm-r*s144,3,0)
p.0y.4=p.0y.3
p.0x.5=format(xm-r*s72,3,0)
p.0y.5=p.0y.2
Do i=1 To 5
Say p.0x.i p.0y.i
End
Call line p.0x.1,p.0y.1,p.0x.3,p.0y.3
Call line p.0x.1,p.0y.1,p.0x.4,p.0y.4
Call line p.0x.2,p.0y.2,p.0x.4,p.0y.4
Call line p.0x.2,p.0y.2,p.0x.5,p.0y.5
Call line p.0x.3,p.0y.3,p.0x.5,p.0y.5

Do i=1 To z.0
s=s||z.i
End

Call lineout pentagram,s
Call lineout pentagram
Exit

lend:
Return reverse(d2c(arg(1),4))

line: Procedure Expose z. red green blue
Parse Arg x0, y0, x1, y1
Say 'line'  x0  y0  x1  y1
dx = abs(x1-x0)
dy = abs(y1-y0)
if x0 < x1 then sx = 1
else sx = -1
if y0 < y1 then sy = 1
else sy = -1
err = dx-dy

Do Forever
xxx=x0*3+2
Do yy=y0-1 To y0+1
z.yy=overlay(copies(blue,5),z.yy,xxx)
End
if x0 = x1 & y0 = y1 Then Leave
e2 = 2*err
if e2 > -dy then do
err = err - dy
x0 = x0 + sx
end
if e2 < dx then do
err = err + dx
y0 = y0 + sy
end
end
Return
::requires RxMath Library
```

## Perl

```use SVG;

my \$tau   = 2 * 4*atan2(1, 1);
my \$dim   = 200;
my \$sides = 5;

for \$v (0, 2, 4, 1, 3, 0) {
push @vx, 0.9 * \$dim * cos(\$tau * \$v / \$sides);
push @vy, 0.9 * \$dim * sin(\$tau * \$v / \$sides);
}

my \$svg= SVG->new( width => 2*\$dim, height => 2*\$dim);

my \$points = \$svg->get_path(
x     => \@vx,
y     => \@vy,
-type => 'polyline',
);

\$svg->rect (
width  => "100%",
height => "100%",
style  => {
'fill' => 'bisque'
}
);

\$svg->polyline (
%\$points,
style => {
'fill'         => 'seashell',
'stroke'       => 'blue',
'stroke-width' => 3,
},
transform => "translate(\$dim,\$dim) rotate(-18)"
);

open  \$fh, '>', 'pentagram.svg';
print \$fh  \$svg->xmlify(-namespace=>'svg');
close \$fh;
```

Pentagram (offsite image)

## Phix

Resizable and optionally rotating gui (desktop) version

Library: Phix/pGUI
Library: Phix/online

You can run this online here.

```--
-- demo\rosetta\Pentagram.exw
-- ==========================
--
-- Start/stop rotation by pressing space. Resizeable.
-- ZXYV stop any rotation and orient up/down/left/right.
--
with javascript_semantics
include pGUI.e

Ihandle dlg, canvas, timer
cdCanvas cdcanvas

integer rot = 0
enum FILL,BORDER
constant colours = {CD_BLUE,CD_RED},
modes = {CD_FILL,CD_CLOSED_LINES}

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, /*posy*/)
integer {w, h} = IupGetIntInt(canvas, "DRAWSIZE"),
cx = floor(w/2),
cy = floor(h/2),
cdCanvasActivate(cdcanvas)
cdCanvasClear(cdcanvas)
cdCanvasSetFillMode(cdcanvas, CD_WINDING)
for mode=FILL to BORDER do
cdCanvasSetForeground(cdcanvas,colours[mode])
cdCanvasBegin(cdcanvas,modes[mode])
for a=90 to 666 by 144 do
cdCanvasVertex(cdcanvas, x, y)
end for
cdCanvasEnd(cdcanvas)
end for
cdCanvasFlush(cdcanvas)
return IUP_DEFAULT
end function

function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cdCanvasSetBackground(cdcanvas, CD_PARCHMENT)
return IUP_DEFAULT
end function

function timer_cb(Ihandle /*ih*/)
rot = mod(rot+359,360)
IupRedraw(canvas)
return IUP_IGNORE
end function

function key_cb(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
c = upper(c)
if c=' ' then
IupSetInt(timer,"RUN",not IupGetInt(timer,"RUN"))
else
c = find(c,"ZYXV")
if c then
IupSetInt(timer,"RUN",false)
rot = (c-1)*90
IupRedraw(canvas)
end if
end if
return IUP_CONTINUE
end function

procedure main()
IupOpen()
canvas = IupCanvas("RASTERSIZE=640x640")
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
dlg = IupDialog(canvas,`TITLE="Pentagram"`)
IupSetCallback(dlg, "KEY_CB", Icallback("key_cb"))
IupShow(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL)
timer = IupTimer(Icallback("timer_cb"), 80, active:=false)
if platform()!=JS then
IupMainLoop()
IupClose()
end if
end procedure

main()
```

And a quick svg version, output identical to sidef

Translation of: Sidef
```without js
constant HDR = """
<?xml version="1.0" standalone="no" ?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN"
"http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd">
<svg height="%d" width="%d" style="" xmlns="http://www.w3.org/2000/svg">
<rect height="100%%" width="100%%" style="fill:black;" />
"""
constant LINE = """
<polyline points="%s"
style="fill:blue; stroke:white; stroke-width:3;"
transform="translate(%d, %d) rotate(-18)" />
"""

function pentagram(integer dim=200, sides=5)

sequence v = repeat(0,sides)
for i=1 to sides do
atom theta = PI*2*(i-1)/5,
x = cos(theta)*dim,
y = sin(theta)*dim
v[i] = {sprintf("%.3f",x),
sprintf("%.3f",y)}
end for
v = append(v,v[1])
sequence q = {}
for i=1 to length(v) by 2 do
q &= v[i]
end for
for i=2 to length(v) by 2 do
q &= v[i]
end for
string res = sprintf(HDR,dim*2)
res &= sprintf(LINE,{join(q),dim,dim})
res &= "</svg>\n"

return res
end function

puts(1,pentagram())
```

## PostScript

```%!PS-Adobe-3.0 EPSF
%%BoundingBox: 0 0 200 600

/n 5 def % 5-star; can be set to other odd numbers

/s { gsave } def
/r { grestore } def
/g { .7 setgray } def
/t { 100 exch translate } def
/p {
180 90 n div sub rotate
0 0 moveto
n { 0 160 rlineto 180 180 n div sub rotate } repeat
closepath
} def

s 570 t p s g eofill r stroke r		% even-odd fill
s 370 t p s g fill r stroke r		% non-zero fill
s 170 t p s 2 setlinewidth stroke r g fill r % non-zero, but hide inner strokes

%%EOF
```

The following isn't exactly what the task asks for, but it's kind of fun if you have a PS interpreter that progressively updates. The program draws a lot of stars, so it's extremely likely that some of them are pentagrams...

```%!PS-Adobe-3.0 EPSF
%%BoundingBox: 0 0 400 400

% randomly choose from 5- to 35-stars
/maxpoint 35 def
/minpoint 5 def

/rnd1 { rand 16#80000000 div } def
/rnd { rnd1 mul} def
/rndi { 2 index sub rnd1 mul 1 index div cvi mul add} def
/line { rotate 0 rlineto } def

/star { gsave
/n minpoint 2 maxpoint rndi def
/a 180 180 n div sub def
/b 360 a n mul sub n div def

400 rnd 400 rnd translate 360 rnd rotate
0 0 moveto n { r a line r b line } repeat closepath
rnd1 rnd1 rnd1 3 { 2 index 1 exch sub } repeat
gsave setrgbcolor fill grestore setrgbcolor stroke
grestore } def

0 setlinewidth 2000 {star} repeat showpage
%%EOF
```

## Processing

```//Aamrun, 29th June 2022

size(1000,1000);

translate(width/2,height/2);
rotate(3*PI/2);
fill(#0000ff);

beginShape();
for(int i=0;i<10;i+=2){

vertex(450*cos(i*2*PI/5),450*sin(i*2*PI/5));
}
endShape(CLOSE);
```

## Python

Works with: Python version 3.4.1
```import turtle

turtle.bgcolor("green")
t = turtle.Turtle()
t.color("red", "blue")
t.begin_fill()
for i in range(0, 5):
t.forward(200)
t.right(144)
t.end_fill()
```

## Quackery

```[ \$ "turtleduck.qky" loadfile ] now!

[ [ 1 1
30 times
[ tuck + ]
swap join ] constant
do ]                is phi       (    --> n/d )

[ 5 times
[ 2dup walk
1 5 turn
2dup walk
3 5 turn ]
2drop ]             is star      ( n/d -->     )

[ 5 times
[ 2dup walk
2 5 turn ]
2drop ]             is pentagram ( n/d -->     )

turtle
' [ 79 126 229 ] fill [ 200 1 star ]
10 wide
-1 10 turn
200 1 phi v* phi v* pentagram
1 10 turn```
Output:

## R

Very simple approach,

```p <- cbind(x = c(0, 1, 2,-0.5  , 2.5  ,0),
y = c(0, 1, 0,0.6, 0.6,0))
plot(p)
lines(p)
```

### Using circle equation

A better more accurate approach utilising equation of a circle using polar coordinates.[1] 5 points are required to draw a pentagram. a circle with centre coordinates x=10 and y=10 with radius 10 was chosen for this example. In order to find 5 equal points circle needs to be divided by 5 i.e 360/5 = 72 each point on the circumference is 72 degrees apart, 5 points on the circles circumference are calculated and than plotted and line drawn in-between to produce pentagram

```#Circle equation
#x = r*cos(angle) + centre_x
#y = r*sin(angle) + centre_y

#centre points
centre_x = 10
centre_y = 10
r = 10

return((d*pi)/180)
X_coord <- function(r=10,centre_x=10,angle) #Finds Xcoordinate on the circumference
{
}
Y_coord <- function(r=10,centre_y=10,angle) #Finds Ycoordinate on the circumference
{
}

# series of angles after dividing the circle in to 5
angles <- list()
for(i in 1:5)
{
angles[i] <- 72*i
}
angles <- unlist(angles) #flattening the list

for(i in seq_along(angles)){
print(i)
print(angles[i])
if(i == 1)
{
coordinates <-
cbind(c(
x = X_coord(angle = angles[i]),
y = Y_coord(angle = angles[i]))
)
}
else{
coordinates <- cbind(coordinates,cbind(c(
x = X_coord(angle = angles[i]),
y = Y_coord(angle = angles[i]))))
}
}
plot(xlim = c(0,30), ylim = c(0,30),x = coordinates[1,], y=coordinates[2,])

polygon(x = coordinates[1,c(1,3,5,2,4,1)],
y=coordinates[2,c(1,3,5,2,4,1)],
col = "#1b98e0",
border = "red",
lwd = 5)
```

## Racket

```#lang racket
(require 2htdp/image)

(overlay
(star-polygon 100 5 2 "outline" (make-pen "blue" 4 "solid" "round" "round"))
(star-polygon 100 5 2 "solid" "cyan"))
```

## Raku

(formerly Perl 6)

Works with: rakudo version 2018.08

Generate an SVG file to STDOUT. Redirect to a file to capture and display it.

```use SVG;

constant \$dim = 200;
constant \$sides = 5;

my @vertices = map { 0.9 * \$dim * cis(\$_ * τ / \$sides) }, ^\$sides;

my @points   = map |*.reals.fmt("%0.3f"),
flat @vertices[0, 2 ... *], @vertices[1, 3 ... *], @vertices[0];

say SVG.serialize(
svg => [
:width(\$dim*2), :height(\$dim*2),
:rect[:width<100%>, :height<100%>, :style<fill:bisque;>],
:polyline[ :points(@points.join: ','),
:style("stroke:blue; stroke-width:3; fill:seashell;"),
:transform("translate(\$dim,\$dim) rotate(-90)")
],
],
);
```

See Pentagram (offsite svg image)

Ever wondered what a regular 7 sided star looks like? Change \$sides to 7 and re-run. See Heptagram

## Red

```Red [
Source:     https://github.com/vazub/rosetta-red
Tabs:       4
Needs:       'View
]

canvas: 500x500
center: as-pair canvas/x / 2 canvas/y / 2

points: collect [
repeat vertex 10 [
angle: vertex * 36 + 18 ;-- +18 is required for pentagram rotation
either vertex // 2 = 1 [
keep as-pair (cosine angle) * radius + center/x (sine angle) * radius + center/y
][
keep as-pair (cosine angle) * radius * 0.382 + center/x (sine angle) * radius * 0.382 + center/y
]
]
]

view [
title "Pentagram"
base canvas white
draw compose/deep [
fill-pen mint
polygon (points)
line-width 3
line (points/1) (points/5) (points/9) (points/3) (points/7) (points/1)
]
]
```

## REXX

Translation of: ooRexx
```/* REXX ***************************************************************
* Create a BMP file showing a pentagram
**********************************************************************/
Parse Version v
If pos('Regina',v)>0 Then
pentagram='pentagrama.bmp'
Else
pentagram='pentagramx.bmp'
'erase' pentagram
s='424d4600000000000000360000002800000038000000280000000100180000000000'X||,
'1000000000000000000000000000000000000000'x
Say 'sl='length(s)
z.0=0
white='ffffff'x
red  ='00ff00'x
green='ff0000'x
blue ='0000ff'x
rd6=copies(rd,6)
m=133
m=80
n=80
hor=m*8      /* 56 */
ver=n*8      /* 40 */
Say 'hor='hor
Say 'ver='ver
Say 'sl='length(s)
s=overlay(lend(hor),s,19,4)
s=overlay(lend(ver),s,23,4)
Say 'sl='length(s)
z.=copies('ffffff'x,3192%3)
z.=copies('ffffff'x,8*m)
z.0=648
pi_5=2*3.14159/5
s72 =sin(pi_5  )
c72 =cos(pi_5  )
s144=sin(pi_5*2)
c144=cos(pi_5*2)
xm=300
ym=300
r=200
p.0x.1=xm
p.0y.1=ym+r

p.0x.2=format(xm+r*s72,3,0)
p.0y.2=format(ym+r*c72,3,0)
p.0x.3=format(xm+r*s144,3,0)
p.0y.3=format(ym+r*c144,3,0)
p.0x.4=format(xm-r*s144,3,0)
p.0y.4=p.0y.3
p.0x.5=format(xm-r*s72,3,0)
p.0y.5=p.0y.2
Do i=1 To 5
Say p.0x.i p.0y.i
End
Call line p.0x.1,p.0y.1,p.0x.3,p.0y.3
Call line p.0x.1,p.0y.1,p.0x.4,p.0y.4
Call line p.0x.2,p.0y.2,p.0x.4,p.0y.4
Call line p.0x.2,p.0y.2,p.0x.5,p.0y.5
Call line p.0x.3,p.0y.3,p.0x.5,p.0y.5

Do i=1 To z.0
s=s||z.i
End

Call lineout pentagram,s
Call lineout pentagram
Exit

lend:
Return reverse(d2c(arg(1),4))

line: Procedure Expose z. red green blue
Parse Arg x0, y0, x1, y1
Say 'line'  x0  y0  x1  y1
dx = abs(x1-x0)
dy = abs(y1-y0)
if x0 < x1 then sx = 1
else sx = -1
if y0 < y1 then sy = 1
else sy = -1
err = dx-dy

Do Forever
xxx=x0*3+2
Do yy=y0-1 To y0+1
z.yy=overlay(copies(blue,5),z.yy,xxx)
End
if x0 = x1 & y0 = y1 Then Leave
e2 = 2*err
if e2 > -dy then do
err = err - dy
x0 = x0 + sx
end
if e2 < dx then do
err = err + dx
y0 = y0 + sy
end
end
Return

sin: Procedure
/* REXX ****************************************************************
* Return sin(x<,p>) -- with the specified precision
***********************************************************************/
Parse Arg x,prec
If prec='' Then prec=9
Numeric Digits (2*prec)
Numeric Fuzz   3
pi=3.14159
Do While x>pi
x=x-pi
End
Do While x<-pi
x=x+pi
End
o=x
u=1
r=x
Do i=3 By 2
ra=r
o=-o*x*x
u=u*i*(i-1)
r=r+(o/u)
If r=ra Then Leave
End
Numeric Digits prec
Return r+0

cos: Procedure
/* REXX ****************************************************************
* Return cos(x) -- with specified precision
***********************************************************************/
Parse Arg x,prec
If prec='' Then prec=9
Numeric Digits (2*prec)
Numeric Fuzz 3
o=1
u=1
r=1
Do i=1 By 2
ra=r
o=-o*x*x
u=u*i*(i+1)
r=r+(o/u)
If r=ra Then Leave
End
Numeric Digits prec
Return r+0

sqrt: Procedure
/* REXX ***************************************************************
* EXEC to calculate the square root of a = 2 with high precision
**********************************************************************/
Parse Arg x,prec
If prec<9 Then prec=9
prec1=2*prec
eps=10**(-prec1)
k = 1
Numeric Digits 3
r0= x
r = 1
Do i=1 By 1 Until r=r0 | (abs(r*r-x)<eps)
r0 = r
r  = (r + x/r) / 2
k  = min(prec1,2*k)
Numeric Digits (k + 5)
End
Numeric Digits prec
Return r+0
```

## Ring

```# Project : Pentagram

paint = null

new qapp
{
win1 = new qwidget() {
setwindowtitle("Pentagram")
setgeometry(100,100,500,600)
label1 = new qlabel(win1) {
setgeometry(10,10,400,400)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,500,100,30)
settext("draw")
setclickevent("draw()")
}
show()
}
exec()
}

func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(5)
}
paint = new qpainter() {
begin(p1)
setpen(pen)

nn = 165
cx = 800
cy = 600
phi = 54

color = new qcolor()
color.setrgb(0, 0, 255,255)
mybrush = new qbrush() {setstyle(1) setcolor(color)}
setbrush(mybrush)

for n = 1 to 5
theta = fabs(180-144-phi)
p1x = floor(cx + nn * cos(phi * 0.01745329252))
p1y = floor(cy + nn * sin(phi * 0.01745329252))
p2x = floor(cx - nn * cos(theta * 0.01745329252))
p2y = floor(cy - nn * sin(theta * 0.01745329252))
phi+= 72
drawpolygon([[p1x,p1y],[cx,cy],[p2x,p2y]],0)
next

endpaint()
}
label1 { setpicture(p1) show() }
return```

Output:

## Scala

### Java Swing Interoperability

```import java.awt._
import java.awt.geom.Path2D

import javax.swing._

object Pentagram extends App {

SwingUtilities.invokeLater(() =>
new JFrame("Pentagram") {

class Pentagram extends JPanel {
setPreferredSize(new Dimension(640, 640))
setBackground(Color.white)
final private val degrees144 = Math.toRadians(144)

override def paintComponent(gg: Graphics): Unit = {
val g = gg.asInstanceOf[Graphics2D]

def drawPentagram(g: Graphics2D, x: Int, y: Int, fill: Color): Unit = {
var (_x, _y, angle) = (x, y, 0.0)
val p = new Path2D.Float
p.moveTo(_x, _y)
for (i <- 0 until 5) {
val (x2, y2) = (_x + (Math.cos(angle) * 500).toInt, _y + (Math.sin(-angle) * 500).toInt)
p.lineTo(x2, y2)
_x = x2
_y = y2
angle -= degrees144
}
p.closePath()
g.setColor(fill)
g.fill(p)
g.setColor(Color.darkGray)
g.draw(p)
}

super.paintComponent(gg)
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
g.setStroke(new BasicStroke(5, BasicStroke.CAP_ROUND, BasicStroke.JOIN_MITER))
drawPentagram(g, 70, 250, new Color(0x6495ED))
}
}

pack()
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
setLocationRelativeTo(null)
setResizable(false)
setVisible(true)
}
)

}
```

## Sidef

Translation of: Raku

Generates a SVG image to STDOUT.

```func pentagram(dim=200, sides=5) {
var pentagram = <<-EOT
<?xml version="1.0" standalone="no" ?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN"
"http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd">
<svg height="#{dim*2}" width="#{dim*2}" style="" xmlns="http://www.w3.org/2000/svg">
<rect height="100%" width="100%" style="fill:black;" />
EOT

func pline(q) {
<<-EOT
<polyline points="#{{|n| '%0.3f' % n }.map(q, q[0], q[1]).join(' ')}"
style="fill:blue; stroke:white; stroke-width:3;"
transform="translate(#{dim}, #{dim}) rotate(-18)" />
EOT
}

var v = {|k| 0.9 * dim * cis(k * Num.tau / sides) }.map(^sides)
pentagram += pline([v[range(0, v.end, 2)], v[range(1, v.end, 2)]].map{.reals})
pentagram += '</svg>'

return pentagram
}

say pentagram()
```
Output:
```<?xml version="1.0" standalone="no" ?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN"
"http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd">
<svg height="400" width="400" style="" xmlns="http://www.w3.org/2000/svg">
<rect height="100%" width="100%" style="fill:black;" />
<polyline points="180.000 0.000 -145.623 105.801 55.623 -171.190 55.623 171.190 -145.623 -105.801 180.000 0.000"
style="fill:blue; stroke:white; stroke-width:3;"
transform="translate(200, 200) rotate(-18)" />
</svg>```

## SPL

```mx,my = #.scrsize()
xc = mx/2
yc = my/2
mr = #.min(mx,my)/3
#.angle(#.degrees)
#.drawcolor(1,0,0)
#.drawsize(10)
> r, mr..0,-1
#.drawline(xc,yc-r,xc,yc-r)
> a, 54..630,144
#.drawline(r*#.cos(a)+xc,r*#.sin(a)+yc)
<
#.drawcolor(1,1,0)
#.drawsize(1)
<```

## Tcl

This implementation draws a simple pentagram on a Canvas widget.

Works with: Tcl version 8.6
```package require Tk 8.6   	;# lmap is new in Tcl/Tk 8.6

set pi [expr 4*atan(1)]

pack [canvas .c] -expand yes -fill both     ;# create the canvas

update          ;# draw everything so the dimensions are accurate

set w [winfo width .c]          ;# calculate appropriate dimensions
set h [winfo height .c]
set r [expr {min(\$w,\$h) * 0.45}]

set points [lmap n {0 1 2 3 4 5} {
set n [expr {\$n * 2}]
set y [expr {sin(\$pi * 2 * \$n / 5) * \$r + \$h / 2}]
set x [expr {cos(\$pi * 2 * \$n / 5) * \$r + \$w / 2}]
list \$x \$y
}]
set points [concat {*}\$points]  ;# flatten the list

puts [.c create line \$points]

;# a fun reader exercise is to make the shape respond to mouse events,
;# or animate it!
```

## Wren

Translation of: Go
Library: DOME
```import "graphics" for Canvas, Color, Point
import "dome" for Window

class Game {
static init() {
Window.title = "Pentagram"
var width = 640
var height = 640
Window.resize(width, height)
Canvas.resize(width, height)
Canvas.cls(Color.white)
var col = Color.hex("#6495ed") // cornflower blue
for (i in 1..240) pentagram(320, 320, i, col)
for (i in 241..250) pentagram(320, 320, i, Color.black)
}

static update() {}

static draw(alpha) {}

static pentagram(x, y, r, col) {
var points = List.filled(5, null)
for (i in 0..4) {
var angle = 2*Num.pi*i/5 - Num.pi/2
points[i] = Point.new(x + r*angle.cos, y + r*angle.sin)
}
var prev = points[0]
for (i in 1..5) {
var index = (i * 2) % 5
var curr = points[index]
Canvas.line(prev.x, prev.y, curr.x, curr.y, col)
prev = curr
}
}
}
```

## XPL0

```proc    FillArea(X, Y, C0, C);  \Replace area colored C0 with color C
int     X, Y,   \starting coordinate for flood fill algorithm
C0, C;  \initial color, and color to replace it with
def     S=8000; \size of queue (must be an even number)
int     Q(S),   \queue (FIFO)
F, E;   \fill and empty indexes

proc    EnQ(X, Y);      \Enqueue coordinate
int     X, Y;
[Q(F):= X;
F:= F+1;
Q(F):= Y;
F:= F+1;
if F >= S then F:= 0;
];      \EnQ

proc    DeQ;            \Dequeue coordinate
[X:= Q(E);
E:= E+1;
Y:= Q(E);
E:= E+1;
if E >= S then E:= 0;
];      \DeQ

[if C0 = C then return;
F:= 0;  E:= 0;
EnQ(X, Y);
while E # F do
[DeQ;
if ReadPix(X, Y) = C0 then
[Point(X, Y, C);
EnQ(X-1, Y);
EnQ(X, Y+1);
EnQ(X, Y-1);
];
];
];      \FillArea

def     Size = 200.;
def     Pi = 3.141592654;
def     Deg144 = 4.*Pi/5.;
int     X, Y, N;
[SetVid(\$12);           \set 640x480x4 VGA graphics
for Y:= 0 to 480-1 do   \fill screen
[Move(0, Y);  Line(640-1, Y, \$F\white\)];
for N:= 0 to 5 do       \draw pentagram
[X:= fix(Size*Sin(float(N)*Deg144));
Y:= fix(Size*Cos(float(N)*Deg144));
if N = 0 then Move(X+320, 240-Y)
else Line(X+320, 240-Y, 4\red\);
];
FillArea(0, 0, \$F, 1);  \replace white (F) with blue (1)
]```

## zkl

 This example is incorrect. It does not accomplish the given task. Please fix the code and remove this message.
Translation of: Raku

Generate an SVG file to STDOUT. Redirect to a file to capture and display it.

```const DIM=200, SIDES=5, A=360/SIDES, R=DIM.toFloat();
#<<<
0'|<?xml version="1.0" standalone="no" ?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN"
"http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd">
<svg height="%d" width="%d" style="" xmlns="http://www.w3.org/2000/svg">
<rect height="100%" width="100%" style="fill:bisque;" />|
#<<<
.fmt(DIM*2, DIM*2).println();

var vertices=vs.pump(List,fcn(a){ R.toRectangular(a) }); //( (x,y), (x,y)...
SIDES.pump(String,pline).println();  // the line pairs that draw the pentagram

fcn pline(n){ a:=(n + 2)%SIDES; // (n,a) are the endpoints of the right leg
pts:=String("\"", ("% 0.3f,% 0.3f "*2), "\" "); // two points
vs:='wrap(){ T(n,a).pump(List,vertices.get).flatten() }; //(x,y, x,y)
String(
(0'|<polyline points=| + pts).fmt(vs().xplode()),
0'|style="fill:seashell; stroke:blue; stroke-width:3;" |,
0'|transform="translate(%d,%d) rotate(-18)"|.fmt(DIM,DIM),
" />\n"
);
}
println("</svg>");```
Output:
```\$ zkl bbb > pentagram.svg
\$ cat pentagram.svg
<?xml version="1.0" standalone="no" ?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.0//EN"
"http://www.w3.org/TR/2001/PR-SVG-20010719/DTD/svg10.dtd">
<svg height="400" width="400" style="" xmlns="http://www.w3.org/2000/svg">
<rect height="100%" width="100%" style="fill:bisque;" />
<polyline points=" 200.000, 0.000 -161.803, 117.557 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" />
<polyline points=" 61.803, 190.211 -161.803,-117.557 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" />
<polyline points="-161.803, 117.557  61.803,-190.211 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" />
<polyline points="-161.803,-117.557  200.000, 0.000 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" />
<polyline points=" 61.803,-190.211  61.803, 190.211 " style="fill:seashell; stroke:blue; stroke-width:3;" transform="translate(200,200) rotate(-18)" />

</svg>
```