Textfeld: Tell me if you know better solutions.
CL=cut length if polygon side is 1
2 pieces 3 pieces 4 pieces
T5
2008
5 pieces
6 pieces
T2
 
T3
T4
 
   
CL=0.6734+ CL=0.8660+ CL=1.3051+ CL=1.5803+ CL=1.7321+
S4
S2
1
 
   
S5
Textfeld: formula
S6
Textfeld: data
2008
 
CL=1.0000 CL=1.6233+ CL=1.9755+ CL=2.5021+ CL=2.9399+
 
Textfeld: formula
P3
Textfeld: formula
P4
P5
Textfeld: data
 
Textfeld: formula
P6
CL=1.4310+ CL=2.1587+ CL=2.8340+ CL=3.3383+ CL=3.7420+
H2
 
H3
H4
H5
Textfeld: formula
H6
CL=1.7321+ CL=2.5981+ CL=3.4641+ CL=4.3301+ CL=4.9137+
Hp4
Hp6
Hp3
Textfeld: formula
Hp2
Textfeld: formula
Hp5
Textfeld: data
Textfeld: data
 
       
CL=1.8351+ CL=3.1828+ CL=4.1800+ CL=5.1985+ CL=5.7635+
Principles for constructing equal area dissections with minimal cut length
straight lines or circle arcs
vertices with only 3 edges
equal angle vertices, 120
joining border with right angle
Laplace rule: sum of signed curvatures at vertex is zero
I got very valuable hints from Warren D. Smith, 13.8.2007.
Textfeld: Here you can find findings on CIRCLES instead of polygons
The findings can nicely be verified with soap bubbles with well defined confinement and monolayers. See one picture for S6 from J.Reber.
Warren D. Smith
Zoomable pictures in pdf
Competitors: Download of postscript pictures 15KB
T5b
 
T5c
T5d
arcs
Textfeld: data
 
CL=1.6166+ ? CL=1.6145+ CL=1.3817+ CL=1.6037+
 
P2b
P4a
Textfeld: formula
P3a
S4a
Textfeld: data
 
CL=1.3422+ CL=1.5388+ CL=2.8485+ CL=2.2057+ CL=2.4192+
T4c
Hall
 
P4c
P4b
P4e
S6a
Textfeld: data
 
CL=1.3173+ ? CL=2.9699+ CL=2.8587+ CL=2.9484+
P5a
 
P5b
Textfeld: data
 
P5c
P2a
S6b
CL=3.4410+ CL=3.5337+ CL=3.3892+ CL=1.4553+ CL=3.0000
 
H5a
H5b
Textfeld: data
 
H6b
S6c
CL=2.9942+ CL=4.3541+ CL=4.3808+ ? ?
H6a
 
H6d
H7a
 
H4a
Hp4a
 
CL=5.1962+ CL=5.1962+ CL=5.1962+ CL=3.7321+ CL=4.2201+
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