BookmarkSubscribeRSS Feed
☑ This topic is solved. Need further help from the community? Please sign in and ask a new question.
Rick_SAS
SAS Super FREQ

In the spirit of Pi Day, and motivated by the great holiday posts by @tc, I thought I'd post a challenge for the graphics gurus. While writing a Pi Day blog post about how Isaac Newton approximated pi to 16 decimals places, I needed to create a diagram that shows the geometry that Newton used in the calculation. I was in a hurry, so I used PowerPoint to create the image.

 

My challenge: Can you create the image by using PROC SGPLOT (or the GTL)?

 

I'll give you a hint: Archimedes knew that you could approximate a circle to any accuracy by using a polygon with many sid...

 

To keep it simple, you do NOT have to use the square-root symbol in your plot; use 'sqrt(3)' instead.

Here's the figure from my Pi Day post. Good luck!

 

NewtonPi1.png

 

1 ACCEPTED SOLUTION

Accepted Solutions
Ksharp
Super User
/*I forgot the vertical symbol*/
data have;
id1=1;
do theta=0 to constant('pi') by 0.01;
 x=0.5*cos(theta)+0.5; y=0.5*sin(theta);output;
end;

id2=1;
do theta=0 to (2/3)*constant('pi') by 0.01;
 _x=0.5*cos(theta)+0.5; _y=0.5*sin(theta);output;
end;
_x=0.25;_y=0;output;

x1=0.5;  y1=0.66;output;
x1=1.32; y1=0;output;

x2=0.5; y2=0;datalabel='C';output;
x2=0;   y2=0;datalabel='O';output;
x2=0.25;y2=0;datalabel='A';output;
x3=0.25;y3=sqrt(3)/4;datalabel='B';output;

id3=1;x4=0.3;y4=0.05;output;
id3=1;x4=0.3;y4=0;output;
id3=2;x4=0.3;y4=0.05;output;
id3=2;x4=0.25;y4=0.05;output;

run;


%sganno

data sganno;
 %SGARROW( X1=0, Y1=0,X2=0,Y2=100,DIRECTION= "OUT",X1SPACE="DATAVALUE",Y2SPACE="WALLPERCENT",
            X2SPACE="DATAVALUE",Y1SPACE="DATAVALUE",LINECOLOR="blue" ,SHAPE="BARBED" )
 %SGARROW( X1=0, Y1=0,X2=100,Y2=0,DIRECTION= "OUT",X1SPACE="DATAVALUE",Y2SPACE="DATAVALUE",
            X2SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",LINECOLOR="blue" ,SHAPE="BARBED" )

%SGTEXT( LABEL="O",ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0, Y1=0, WIDTH=12)
%SGTEXT(LABEL="0", ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0,Y1=-0.05,WIDTH=12)

%SGTEXT( LABEL="A",ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.25, Y1=0, WIDTH=12)
%SGTEXT(LABEL="1/4", ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.25,Y1=-0.05,WIDTH=12)

%SGTEXT( LABEL="C  ",ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.5, Y1=0, WIDTH=12)
%SGTEXT(LABEL="1/2", ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.5,Y1=-0.05,WIDTH=12)

%SGTEXT(LABEL="M", ANCHOR="BOTTOM" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.125,Y1=0.1,WIDTH=12,FILLCOLOR="white")
%SGTEXT(LABEL="r = 1/2", ANCHOR="BOTTOMLEFT" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.4,Y1=0.2,WIDTH=12)
%SGTEXT( LABEL="x",ANCHOR="TOP" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=95, Y1=0, WIDTH=12,FILLTRANSPARENCY=1)
%SGTEXT( LABEL="y",ANCHOR="RIGHT" , X1SPACE="DATAVALUE",Y1SPACE="WALLPERCENT",TEXTSIZE= 12,X1=0, Y1=90, WIDTH=12,FILLTRANSPARENCY=1)
%SGTEXT( LABEL="3/4  ",ANCHOR="RIGHT" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=0, Y1=0.433, WIDTH=12,FILLTRANSPARENCY=1)

%SGTEXT( LABEL="(*ESC*){unicode '221A'x}",ANCHOR="RIGHT" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=-3, Y1=0.433, WIDTH=12,FILLTRANSPARENCY=1)
%SGTEXT( LABEL="(*ESC*){unicode '2013'x}",ANCHOR="RIGHT" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=-1.7, Y1=0.448, WIDTH=12,FILLTRANSPARENCY=1)

run;


proc sgplot data=have noborder aspect=0.5 sganno=sganno noautolegend pad=(left=40);
polygon id=id1 x=x y=y/fillpattern nofill fillpatternattrs=(color=brown);
polygon id=id2 x=_x y=_y/fill fillattrs=(color=white);

series x=x y=y/smoothconnect lineattrs=(color=blue thickness=2);
scatter x=x1 y=y1/markerattrs=(size=0);

scatter x=x3 y=y3/markerattrs=(symbol=circlefilled) 
        datalabel=datalabel datalabelpos=topleft datalabelattrs=(size=12);
scatter x=x2 y=y2/markerattrs=(symbol=circlefilled) ;
vector x=x3 y=y3/xorigin=0.5 yorigin=0 noarrowheads lineattrs=(color=blue thickness=2);
dropline x=x3 y=y3/dropto=x lineattrs=(pattern=solid color=blue thickness=2) ;
dropline x=x3 y=y3/dropto=y lineattrs=(pattern=shortdash color=blue thickness=2) ;

series x=x4 y=y4/group=id3 lineattrs=(pattern=solid color=blue thickness=2) ;

yaxis offsetmin=0.01 offsetmax=0   label='y' display=none min=-0.006 ;
xaxis offsetmin=0.01 offsetmax=0  label='x' display=none;

run;

Ksharp_0-1678438897635.png

 

View solution in original post

3 REPLIES 3
Ksharp
Super User

Rick,

Finally, I got it worked . It is really uneasy. Have fun with the following code.

 

 

data have;
id1=1;
do theta=0 to constant('pi') by 0.01;
 x=0.5*cos(theta)+0.5; y=0.5*sin(theta);output;
end;

id2=1;
do theta=0 to (2/3)*constant('pi') by 0.01;
 _x=0.5*cos(theta)+0.5; _y=0.5*sin(theta);output;
end;
_x=0.25;_y=0;output;

x1=0.5;  y1=0.66;output;
x1=1.32; y1=0;output;

x2=0.5; y2=0;datalabel='C';output;
x2=0;   y2=0;datalabel='O';output;
x2=0.25;y2=0;datalabel='A';output;
x3=0.25;y3=sqrt(3)/4;datalabel='B';output;
run;


%sganno

data sganno;
 %SGARROW( X1=0, Y1=0,X2=0,Y2=100,DIRECTION= "OUT",X1SPACE="DATAVALUE",Y2SPACE="WALLPERCENT",
            X2SPACE="DATAVALUE",Y1SPACE="DATAVALUE",LINECOLOR="blue" ,SHAPE="BARBED" )
 %SGARROW( X1=0, Y1=0,X2=100,Y2=0,DIRECTION= "OUT",X1SPACE="DATAVALUE",Y2SPACE="DATAVALUE",
            X2SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",LINECOLOR="blue" ,SHAPE="BARBED" )

%SGTEXT( LABEL="O",ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0, Y1=0, WIDTH=12)
%SGTEXT(LABEL="0", ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0,Y1=-0.05,WIDTH=12)

%SGTEXT( LABEL="A",ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.25, Y1=0, WIDTH=12)
%SGTEXT(LABEL="1/4", ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.25,Y1=-0.05,WIDTH=12)

%SGTEXT( LABEL="C  ",ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.5, Y1=0, WIDTH=12)
%SGTEXT(LABEL="1/2", ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.5,Y1=-0.05,WIDTH=12)

%SGTEXT(LABEL="M", ANCHOR="BOTTOM" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.125,Y1=0.1,WIDTH=12,FILLCOLOR="white")
%SGTEXT(LABEL="r = 1/2", ANCHOR="BOTTOMLEFT" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.4,Y1=0.2,WIDTH=12)
%SGTEXT( LABEL="x",ANCHOR="TOP" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=95, Y1=0, WIDTH=12,FILLTRANSPARENCY=1)
%SGTEXT( LABEL="y",ANCHOR="RIGHT" , X1SPACE="DATAVALUE",Y1SPACE="WALLPERCENT",TEXTSIZE= 12,X1=0, Y1=90, WIDTH=12,FILLTRANSPARENCY=1)
%SGTEXT( LABEL="3/4  ",ANCHOR="RIGHT" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=0, Y1=0.433, WIDTH=12,FILLTRANSPARENCY=1)

%SGTEXT( LABEL="(*ESC*){unicode '221A'x}",ANCHOR="RIGHT" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=-3, Y1=0.433, WIDTH=12,FILLTRANSPARENCY=1)
%SGTEXT( LABEL="(*ESC*){unicode '2013'x}",ANCHOR="RIGHT" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=-1.7, Y1=0.448, WIDTH=12,FILLTRANSPARENCY=1)
run;


proc sgplot data=have noborder aspect=0.5 sganno=sganno noautolegend pad=(left=40);
polygon id=id1 x=x y=y/fillpattern nofill fillpatternattrs=(color=brown);
polygon id=id2 x=_x y=_y/fill fillattrs=(color=white);

series x=x y=y/smoothconnect lineattrs=(color=blue thickness=2);
scatter x=x1 y=y1/markerattrs=(size=0);

scatter x=x3 y=y3/markerattrs=(symbol=circlefilled) 
        datalabel=datalabel datalabelpos=topleft datalabelattrs=(size=12);
scatter x=x2 y=y2/markerattrs=(symbol=circlefilled) ;
vector x=x3 y=y3/xorigin=0.5 yorigin=0 noarrowheads lineattrs=(color=blue thickness=2);
dropline x=x3 y=y3/dropto=x lineattrs=(pattern=solid color=blue thickness=2) ;
dropline x=x3 y=y3/dropto=y lineattrs=(pattern=shortdash color=blue thickness=2) ;

yaxis offsetmin=0.01 offsetmax=0   label='y' display=none min=-0.006 ;
xaxis offsetmin=0.01 offsetmax=0  label='x' display=none;

run;

Ksharp_0-1678434332925.png

 

Ksharp
Super User
/*I forgot the vertical symbol*/
data have;
id1=1;
do theta=0 to constant('pi') by 0.01;
 x=0.5*cos(theta)+0.5; y=0.5*sin(theta);output;
end;

id2=1;
do theta=0 to (2/3)*constant('pi') by 0.01;
 _x=0.5*cos(theta)+0.5; _y=0.5*sin(theta);output;
end;
_x=0.25;_y=0;output;

x1=0.5;  y1=0.66;output;
x1=1.32; y1=0;output;

x2=0.5; y2=0;datalabel='C';output;
x2=0;   y2=0;datalabel='O';output;
x2=0.25;y2=0;datalabel='A';output;
x3=0.25;y3=sqrt(3)/4;datalabel='B';output;

id3=1;x4=0.3;y4=0.05;output;
id3=1;x4=0.3;y4=0;output;
id3=2;x4=0.3;y4=0.05;output;
id3=2;x4=0.25;y4=0.05;output;

run;


%sganno

data sganno;
 %SGARROW( X1=0, Y1=0,X2=0,Y2=100,DIRECTION= "OUT",X1SPACE="DATAVALUE",Y2SPACE="WALLPERCENT",
            X2SPACE="DATAVALUE",Y1SPACE="DATAVALUE",LINECOLOR="blue" ,SHAPE="BARBED" )
 %SGARROW( X1=0, Y1=0,X2=100,Y2=0,DIRECTION= "OUT",X1SPACE="DATAVALUE",Y2SPACE="DATAVALUE",
            X2SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",LINECOLOR="blue" ,SHAPE="BARBED" )

%SGTEXT( LABEL="O",ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0, Y1=0, WIDTH=12)
%SGTEXT(LABEL="0", ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0,Y1=-0.05,WIDTH=12)

%SGTEXT( LABEL="A",ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.25, Y1=0, WIDTH=12)
%SGTEXT(LABEL="1/4", ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.25,Y1=-0.05,WIDTH=12)

%SGTEXT( LABEL="C  ",ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.5, Y1=0, WIDTH=12)
%SGTEXT(LABEL="1/2", ANCHOR="TOP" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.5,Y1=-0.05,WIDTH=12)

%SGTEXT(LABEL="M", ANCHOR="BOTTOM" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.125,Y1=0.1,WIDTH=12,FILLCOLOR="white")
%SGTEXT(LABEL="r = 1/2", ANCHOR="BOTTOMLEFT" , DRAWSPACE= "DATAVALUE" ,TEXTSIZE= 12,X1=0.4,Y1=0.2,WIDTH=12)
%SGTEXT( LABEL="x",ANCHOR="TOP" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=95, Y1=0, WIDTH=12,FILLTRANSPARENCY=1)
%SGTEXT( LABEL="y",ANCHOR="RIGHT" , X1SPACE="DATAVALUE",Y1SPACE="WALLPERCENT",TEXTSIZE= 12,X1=0, Y1=90, WIDTH=12,FILLTRANSPARENCY=1)
%SGTEXT( LABEL="3/4  ",ANCHOR="RIGHT" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=0, Y1=0.433, WIDTH=12,FILLTRANSPARENCY=1)

%SGTEXT( LABEL="(*ESC*){unicode '221A'x}",ANCHOR="RIGHT" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=-3, Y1=0.433, WIDTH=12,FILLTRANSPARENCY=1)
%SGTEXT( LABEL="(*ESC*){unicode '2013'x}",ANCHOR="RIGHT" , X1SPACE="WALLPERCENT",Y1SPACE="DATAVALUE",TEXTSIZE= 12,X1=-1.7, Y1=0.448, WIDTH=12,FILLTRANSPARENCY=1)

run;


proc sgplot data=have noborder aspect=0.5 sganno=sganno noautolegend pad=(left=40);
polygon id=id1 x=x y=y/fillpattern nofill fillpatternattrs=(color=brown);
polygon id=id2 x=_x y=_y/fill fillattrs=(color=white);

series x=x y=y/smoothconnect lineattrs=(color=blue thickness=2);
scatter x=x1 y=y1/markerattrs=(size=0);

scatter x=x3 y=y3/markerattrs=(symbol=circlefilled) 
        datalabel=datalabel datalabelpos=topleft datalabelattrs=(size=12);
scatter x=x2 y=y2/markerattrs=(symbol=circlefilled) ;
vector x=x3 y=y3/xorigin=0.5 yorigin=0 noarrowheads lineattrs=(color=blue thickness=2);
dropline x=x3 y=y3/dropto=x lineattrs=(pattern=solid color=blue thickness=2) ;
dropline x=x3 y=y3/dropto=y lineattrs=(pattern=shortdash color=blue thickness=2) ;

series x=x4 y=y4/group=id3 lineattrs=(pattern=solid color=blue thickness=2) ;

yaxis offsetmin=0.01 offsetmax=0   label='y' display=none min=-0.006 ;
xaxis offsetmin=0.01 offsetmax=0  label='x' display=none;

run;

Ksharp_0-1678438897635.png

 

Rick_SAS
SAS Super FREQ

@Ksharp posted a very nice program. Anyone want to solve it without using the annotation facility? 

hackathon24-white-horiz.png

The 2025 SAS Hackathon Kicks Off on June 11!

Watch the live Hackathon Kickoff to get all the essential information about the SAS Hackathon—including how to join, how to participate, and expert tips for success.

YouTube LinkedIn

How to Concatenate Values

Learn how use the CAT functions in SAS to join values from multiple variables into a single value.

Find more tutorials on the SAS Users YouTube channel.

SAS Training: Just a Click Away

 Ready to level-up your skills? Choose your own adventure.

Browse our catalog!

Discussion stats
  • 3 replies
  • 1410 views
  • 9 likes
  • 2 in conversation