Knowledge (XXG)

Largest small octagon

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247: 190: 58:. The exact value of the area of the largest small octagon lies between 0.72686845 and 0.72686849, and is approximately 2.8% larger than the area of the 231: 288: 322: 224: 312: 281: 317: 307: 217: 83: 274: 63: 171: 175: 55: 258: 201: 145: 116: 17: 59: 43: 301: 254: 149: 246: 103:
Audet, Charles; Hansen, Pierre; Messine, Frédéric; Xiong, Junjie (April 1, 2002).
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Graham, R. L (March 1, 1975). "The largest small hexagon".
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is the length of the longest segment joining two of its
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was found in 1975 by finding the roots of a degree-10
282: 225: 8: 289: 275: 232: 218: 167:2010 Toulouse Global Optimization Workshop 138:Journal of Combinatorial Theory, Series A 120: 109:Journal of Combinatorial Theory, Series A 62:. This octagon was found in 2002 using 95: 7: 243: 241: 186: 184: 261:. You can help Knowledge (XXG) by 204:. You can help Knowledge (XXG) by 25: 245: 188: 1: 150:10.1016/0097-3165(75)90004-7 105:"The Largest Small Octagon" 18:Hansen's small octagon 339: 240: 183: 66:algorithms. The optimal 257:-related article is a 122:10.1006/jcta.2001.3225 84:Biggest little polygon 50:. The diameter of a 38:that has the largest 32:largest small octagon 323:Combinatorics stubs 64:global optimization 46:octagons with unit 313:Types of polygons 270: 269: 213: 212: 176:Wolfram MathWorld 27:Geometric concept 16:(Redirected from 330: 291: 284: 277: 249: 242: 234: 227: 220: 198:geometry-related 192: 185: 154: 153: 133: 127: 126: 124: 100: 21: 338: 337: 333: 332: 331: 329: 328: 327: 298: 297: 296: 295: 239: 238: 181: 172:Optimal hexagon 163: 158: 157: 135: 134: 130: 102: 101: 97: 92: 80: 60:regular octagon 28: 23: 22: 15: 12: 11: 5: 336: 334: 326: 325: 320: 318:Geometry stubs 315: 310: 300: 299: 294: 293: 286: 279: 271: 268: 267: 250: 237: 236: 229: 222: 214: 211: 210: 193: 179: 178: 169: 162: 161:External links 159: 156: 155: 144:(2): 165–170. 128: 94: 93: 91: 88: 87: 86: 79: 76: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 335: 324: 321: 319: 316: 314: 311: 309: 308:Combinatorics 306: 305: 303: 292: 287: 285: 280: 278: 273: 272: 266: 264: 260: 256: 255:combinatorics 251: 248: 244: 235: 230: 228: 223: 221: 216: 215: 209: 207: 203: 200:article is a 199: 194: 191: 187: 182: 177: 173: 170: 168: 165: 164: 160: 151: 147: 143: 139: 132: 129: 123: 118: 114: 110: 106: 99: 96: 89: 85: 82: 81: 77: 75: 73: 69: 65: 61: 57: 53: 49: 45: 41: 37: 33: 19: 263:expanding it 252: 206:expanding it 195: 180: 141: 137: 131: 115:(1): 46–59. 112: 108: 98: 31: 29: 302:Categories 90:References 72:polynomial 42:among all 78:See also 56:vertices 48:diameter 68:hexagon 52:polygon 36:octagon 34:is the 44:convex 253:This 196:This 259:stub 202:stub 40:area 30:The 174:at 146:doi 117:doi 304:: 142:18 140:. 113:98 111:. 107:. 74:. 290:e 283:t 276:v 265:. 233:e 226:t 219:v 208:. 152:. 148:: 125:. 119:: 20:)

Index

Hansen's small octagon
octagon
area
convex
diameter
polygon
vertices
regular octagon
global optimization
hexagon
polynomial
Biggest little polygon
"The Largest Small Octagon"
doi
10.1006/jcta.2001.3225
doi
10.1016/0097-3165(75)90004-7
2010 Toulouse Global Optimization Workshop
Optimal hexagon
Wolfram MathWorld
Stub icon
geometry-related
stub
expanding it
v
t
e
Stub icon
combinatorics
stub

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