Broom Space

Author

Eric W. Weisstein
September 14, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Topology/BroomSpace.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BroomSpace.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Code

<<Utilities`Typesetting`

Broom[n_:10,o_:{0,0},l_:1]:=Module[{i},
{
{GrayLevel[.4],Disk[o,l,{0,1/n}]},
Table[Line[{o,o+l{Cos[1/i],Sin[1/i]}}],{i,n}],Line[{o,o+l{1,0}}]
}
]

BroomText[n_:6,o_:{0,0},l_:1]:=Module[{i},
Table[
Text[θ ==If[i==1,1,InlineFraction[1,i]],o+1.03l{Cos[1/i],Sin[1/i]},{-1,0}],{i,n}]
]

Figures

Show[Graphics[{Broom[20],BroomText[6]},AspectRatio->Automatic],PlotRange->All]

FullSimplify[Sum[(1/2)^k,{k,0,n-2}]]

Show[Graphics[
{
Table[
Broom[20,{2-2^(2-n),0},1/2^(n-1)],{n,10}],
Table[Text[(Subscript[B, n-1]),{2-2^(2-n)+1/2^n,-.05}],{n,5}],
Line[{{0,0},{2,0}}],
PointSize[.02],Point[{2,0}]
},
AspectRatio->Automatic],PlotRange->All]