Examples of k

Table PE 1. Examples of Perimeter Efficiency, k

 1. Circle or 90° Ellipse 100.000% 46. ring of 10 pentagons 49.010% 2. Reg Poly, n = 360 99.999% 47. Star Reg Poly, n = 9 47.368% 3. Reg Poly, n = 180 99.995% 48. 5° Ellipse 45.802% 4. Reg Poly, n = 90 99.980% 49. triarc 45.310% 5. Reg Poly, n = 60 99.954% 50. 5 Circles 44.721% 6. Reg Poly, n = 45 99.919% 51. Star Reg Poly n = 10 42.972% 7. Reg Poly, n = 36 99.873% 52. Koch, n = 4 - 2nd Tier 41.490% 8. Reg Poly, n = 30 99.817% 53. 6 Circles 40.825% 9. Reg Poly, n = 24 99.714% 54. Koch, n = 3 - 3rd Tier 40.805% 10. 60° Ellipse 99.614% 55. Star Reg Poly n = 12 36.180% 11. Reg Poly, n = 20 99.587% 56. 9 Circles 33.333% 12. Reg Poly, n = 18 99.490% 57. Koch, n = 3 - 4th Tier 30.891% 13. Reg Poly, n = 15 99.264% 58. Star Reg Poly n = 15 29.187% 14. Reg Poly, n =12 - dodecagon 98.850% 59. Star Reg Poly, n = 16 27.412% 15. Reg Poly, n =10 - decagon 98.330% 60. Koch, n = 4 - 3rd Tier 25.890% 16. Reg Poly, n = 9 - nonagon 97.930% 61. 16 Circles 25.000% 17. 45° Ellipse 97.796% 62. Star Reg Poly, n = 18 24.432% 18. Reg Poly, n = 8 - octagon 97.370% 63. Koch, n = 3 - 5th Tier 23.264% 19. Reg Poly, n = 7 96.540% 64. 16 squares 22.150% 20. *Star Reg Poly, n = 3 95.231% 65. Star Reg Poly, n = 20 22.032% 21. Reg Poly, n = 6 - hexagon 95.230% 66. Star Reg Poly, n = 24 18.406% 22. Reg Poly, n = 5 - pentagon 92.990% 67. 100:1 Rectangle 17.549% 23. 30° Ellipse 91.715% 68. Koch, n = 3 - 6th Tier 17.480% 24. Reg Poly, n = 4 - square 88.623% 69. Koch, n = 4 - 4th Tier 15.850% 25. Star Reg Poly, n = 4 88.623% 70. Star Reg Poly, n = 30 14.755% 26. 3:2 Rectangle 86.832% 71. Koch, n=3 - 7th Tier 13.120% 27. 1.618:1 Rectangle 86.118% 72. Star Reg Poly, n = 36 12.310% 28. 5:3 Rectangle 85.809% 73. 100 Circles 10.000% 29. 2:1 Rectangle 83.554% 74. Star Reg Poly, n = 45 9.857% 30. Reg Poly, n = 3 - eq. triangle 77.760% 75. Koch, n=3 - 8th Tier 9.844% 31. Star Reg Poly, n = 5 77.302% 76. Koch, n=4 - 5th Tier 9.620% 32. 3.14159:1 () Rectangle 75.855% 77. Star Reg Poly, n = 60 7.398% 33. 15° Ellipse 74.241% 78. Koch, n = 3 - 9th Tier 7.384% 34. 4:1 Rectangle 70.898% 79. Koch, n = 4 - 6th Tier 5.800% 35. 2 Circles 70.711% 80. 1000:1 Rectangle 5.599% 36. Koch, n = 3 - 1st Tier 67.390% 81. Star Reg Poly, n = 90 4.935% 37. Star Reg Poly, n = 6 67.339% 82. Koch, n = 4 - 7th Tier 3.490% 38. 10.733° Ellipse & Rectangle 64.870% 83. 1000 Circles 3.162% 39. Koch, n = 4 - 1st Tier 63.910% 84. Star Reg Poly, n = 180 2.468% 40. 10:1 Rectangle 63.271% 85. Koch, n = 4 - 8th Tier 2.100% 41. Star Reg Poly, n = 7 59.236% 86. 10000:1 Rectangle 1.772% 42. 3 Circles 57.735% 87. Koch, n = 4 - 9th Tier 1.260% 43. Koch, n = 3 - 2nd Tier 53.236% 88. Star Reg Poly, n = 360 1.234% 44. Star Reg Poly, n = 8 52.695% 89. 10,000 Circles 1.000% 45. 4 Circles 50.000% 90. Reg Poly, n = 2 - digon 0.000%

*The interior isosceles triangles of a regular polygon are replicated outward in the star version. Consequently, the area of the star version is always twice the area of the original, and the perimeter of the star is 2nr instead of 2nb.

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