code for diagram
>
noheadcircarr:=proc(center,start, angle,text,textsize,textshift,colr)
local arc,dir, HEAD, V1,V2,V3,v1,v2,v3,arccenter, txt,tmp,rad,shift,head:
tmp:=evalf(start-center):
rad:=sqrt(tmp[1]^2+tmp[2]^2):
shift:=argument(tmp[1]+tmp[2]*I):
if evalf(shift) < 0 then shift:=shift+2*Pi: fi:
arc:=plot({[start],[center],[center[1]+rad*cos(shift+t),
center[2]+rad*sin(shift+t),t=0..angle]},thickness=3,
color=colr):
dir:=.05*rad*(-sin(angle+shift)+I*cos(angle+shift)):
HEAD:=rad*[cos(angle+shift),sin(angle+shift)]+center:
dir:=evalc(dir):
v1:=evalc(dir*(I-1)):v2:=evalc(dir*(-I-1)):v3:=0:
V1:=[Re(v1),Im(v1)]:
V2:=[Re(v2),Im(v2)]:
V3:=[Re(v3),Im(v3)]:
arccenter:=center+(rad/2)*[cos(2/3*angle+shift),
sin(2/3*angle+shift)]:
txt:=plots[textplot]([textshift*arccenter[1],
textshift*arccenter[2],text],font=[TIMES,BOLD,textsize]):
head:=plots[polygonplot]([1.5*V1+HEAD,1.5*V2+HEAD,1.5*V3+HEAD],color=colr):
head:=plots[polygonplot]([1.5*V1+HEAD,1.5*V2+HEAD,1.5*V3+HEAD],color=colr):
plots[display]({arc,txt},scaling=constrained): end:
>
smallwedgearcandtext:=noheadcircarr([0,0],[cos(Pi/12.0),
sin(Pi/12.0)], Pi/4,` theta`,14,2.7,blue):
>
smallarcarrow:=circarr([0,0],.75*[cos(Pi/12.0),
sin(Pi/12.0)],Pi/4,`theta`,12,1,blue):
>
>
bigarcarrow:=circarr([0,0]+[2,0],
[cos(Pi/12.0),sin(Pi/12.0)]+[2,0],Pi/4.0,`theta`,12,1,blue):
>
bigwedgearcandtext:=noheadcircarr(([0,0]+[2,0]),
(3*[cos(Pi/12.0),sin(Pi/12.0)]+[2,0]), Pi/4.0,`r*theta`,14,1.7,blue):
bigarc:=noheadcircarr(([0,0]+[2,0]),(3*[cos(Pi/12.0),
sin(Pi/12.0)]+[2,0]), Pi/4.0,`theta`,14,1.7,blue):
>
smallwedge:=plot({[[0,0],[cos(Pi/12.0),sin(Pi/12.0)]], [[0,0],[cos(Pi/4.0+Pi/12.0),sin(Pi/4.0+Pi/12.0)]]},
thickness=2,color=red):
>
bigwedge:=plot({ [([0,0]+[2,0]),3*[cos(Pi/12.0),sin(Pi/12.0)]+[2,0]], [([0,0]+[2,0]),3*[cos(Pi/4.0+Pi/12.0),
sin(Pi/4.0+Pi/12.0)]+[2,0]]},thickness=2,color=red):
> bigarrow:=dbarr([0,0]+[2,0],3*[cos(Pi/12.0),sin(Pi/12.0)]+[2,0], `r`,[.03,0], 16,
>
blue):
smallarrow:=dbarr([0,0],[cos(Pi/12.0),sin(Pi/12.0)], `1`,[.1,0], 14, blue):
>
caption:=plots[textplot](
[0,3,`length of arc = radius times angle (in radians)`],font=[TIMES,BOLD,16],align=RIGHT):
>
plots[display]( {caption,smallarrow,bigarrow,smallarcarrow,
bigarcarrow, smallwedge,bigwedge,bigwedgearcandtext, smallwedgearcandtext },view=[0..6,0..3],axes=none);