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Magic polygon

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489: 659: 79: 106:+1 nodes such that the sum of the three nodes are equal. In their definition, a 3 × 3 magic square can be viewed as a magic 4-gon. There are no magic odd-gons with this definition. 148: 403: 379:
Danniel Dias Augusto; Josimar da Silva Rocha (2019). "Magic Polygons and Degenerated Magic Polygons: Characterization and Properties".
430: 280: 307: 190: 700: 154:-gon and a center point. In this definition, magic polygons of Victoria Jakicic and Rachelle Bouchat can be viewed as P( 404:
https://udayton.edu/artssciences/academics/mathematics/images_and_files/umd_proceedings_files/2018/Jakicic-journal.pdf
317: 290: 260: 528: 478: 423: 83: 72: 724: 453: 533: 587: 582: 523: 693: 416: 719: 513: 8: 623: 125: 252: 686: 674: 554: 380: 359: 592: 503: 313: 286: 256: 358:
Jakicic, Victoria; Bouchat, Rachelle (2018). "Magic Polygons and Their Properties".
508: 334: 618: 566: 561: 198: 670: 628: 463: 245: 219: 68: 56: 713: 458: 17: 638: 608: 518: 468: 167: 378: 78: 666: 633: 613: 309:
Unsolved Problems in Geometry: Unsolved Problems in Intuitive Mathematics
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Danniel Dias Augusto and Josimar da Silva defined the magic polygon P(
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Croft, Hallard T.; Falconer, Kenneth; Guy, Richard K. (2012-12-06).
385: 364: 158:,2) magic polygons. They also defined degenerated magic polygons. 408: 52: 32: 658: 109: 98:
Victoria Jakicic and Rachelle Bouchat defined magic polygons as
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Math Skills: Arithmetic with Introductory Algebra and Geometry
67:-sided polygon add up to a constant. Magic polygons are a 128: 93: 55:with an integers on its sides that all add up to a 244: 142: 711: 305: 357: 694: 424: 110:Magic polygons and degenerated magic polygons 59:. It is where positive integers (from 1 to 701: 687: 431: 417: 38: 384: 363: 312:. Springer Science & Business Media. 242: 77: 712: 412: 653: 278: 185: 183: 13: 438: 14: 736: 397: 332: 282:Even More Mathematical Activities 220:"Perimeter Magic Polygon >k=3" 180: 94:Magic polygon with a center point 657: 487: 243:Staszkow, Ronald (2003-05-01). 372: 351: 326: 299: 285:. Cambridge University Press. 272: 236: 212: 102:-sided regular polygons with 2 71:of other magic shapes such as 1: 529:Prime reciprocal magic square 173: 673:. You can help Knowledge by 7: 335:"Perimeter Magic Triangles" 161: 10: 741: 652: 279:Bolt, Brian (1987-04-09). 191:"Perimeter Magic Polygons" 122:) as a set of vertices of 15: 601: 575: 543:Higher dimensional shapes 542: 534:Most-perfect magic square 496: 485: 446: 588:Pandiagonal magic square 583:Associative magic square 524:Pandiagonal magic square 251:. Kendall Hunt. p.  16:Not to be confused with 49:perimeter magic polygon 39:Perimeter magic polygon 669:-related article is a 144: 90: 82:This displays order 3 224:www.magic-squares.net 145: 81: 126: 624:Eight queens puzzle 267:Magic polygon math. 195:www.trottermath.net 143:{\displaystyle k/2} 140: 91: 725:Mathematics stubs 682: 681: 647: 646: 593:Multimagic square 504:Alphamagic square 333:Heinz, Harvey D. 35:on its vertices. 732: 703: 696: 689: 661: 654: 602:Related concepts 509:Antimagic square 491: 433: 426: 419: 410: 409: 391: 390: 388: 376: 370: 369: 367: 355: 349: 348: 346: 345: 330: 324: 323: 303: 297: 296: 276: 270: 269: 250: 240: 234: 233: 231: 230: 216: 210: 209: 207: 206: 197:. Archived from 187: 149: 147: 146: 141: 136: 47:, also called a 740: 739: 735: 734: 733: 731: 730: 729: 710: 709: 708: 707: 650: 648: 643: 619:Number Scrabble 597: 571: 567:Magic hyperbeam 562:Magic hypercube 538: 514:Geomagic square 492: 483: 442: 437: 400: 395: 394: 377: 373: 356: 352: 343: 341: 331: 327: 320: 304: 300: 293: 277: 273: 263: 241: 237: 228: 226: 218: 217: 213: 204: 202: 189: 188: 181: 176: 164: 132: 127: 124: 123: 112: 96: 84:magic triangles 73:magic triangles 41: 27:is a polygonal 21: 12: 11: 5: 738: 728: 727: 722: 706: 705: 698: 691: 683: 680: 679: 662: 645: 644: 642: 641: 636: 631: 629:Magic constant 626: 621: 616: 611: 605: 603: 599: 598: 596: 595: 590: 585: 579: 577: 576:Classification 573: 572: 570: 569: 564: 559: 558: 557: 546: 544: 540: 539: 537: 536: 531: 526: 521: 516: 511: 506: 500: 498: 497:Related shapes 494: 493: 486: 484: 482: 481: 479:Magic triangle 476: 471: 466: 464:Magic hexagram 461: 456: 450: 448: 444: 443: 440:Magic polygons 436: 435: 428: 421: 413: 407: 406: 399: 398:External links 396: 393: 392: 371: 350: 325: 318: 298: 291: 271: 261: 235: 211: 178: 177: 175: 172: 171: 170: 163: 160: 139: 135: 131: 111: 108: 95: 92: 88:magic polygon. 69:generalization 57:magic constant 40: 37: 9: 6: 4: 3: 2: 737: 726: 723: 721: 720:Magic figures 718: 717: 715: 704: 699: 697: 692: 690: 685: 684: 678: 676: 672: 668: 663: 660: 656: 655: 651: 640: 637: 635: 632: 630: 627: 625: 622: 620: 617: 615: 612: 610: 607: 606: 604: 600: 594: 591: 589: 586: 584: 581: 580: 578: 574: 568: 565: 563: 560: 556: 553: 552: 551: 548: 547: 545: 541: 535: 532: 530: 527: 525: 522: 520: 517: 515: 512: 510: 507: 505: 502: 501: 499: 495: 490: 480: 477: 475: 472: 470: 467: 465: 462: 460: 459:Magic hexagon 457: 455: 452: 451: 449: 445: 441: 434: 429: 427: 422: 420: 415: 414: 411: 405: 402: 401: 387: 382: 375: 366: 361: 354: 340: 336: 329: 321: 319:9781461209638 315: 311: 310: 302: 294: 292:9780521339940 288: 284: 283: 275: 268: 264: 262:9780787292966 258: 254: 249: 248: 239: 225: 221: 215: 201:on 2018-01-12 200: 196: 192: 186: 184: 179: 169: 166: 165: 159: 157: 153: 137: 133: 129: 121: 117: 107: 105: 101: 89: 85: 80: 76: 74: 70: 66: 62: 58: 54: 50: 46: 45:magic polygon 36: 34: 30: 26: 25:magic polygon 19: 18:Polygon Magic 675:expanding it 664: 649: 639:Magic series 609:Latin square 519:Heterosquare 469:Magic square 454:Magic circle 439: 374: 353: 342:. Retrieved 338: 328: 308: 301: 281: 274: 266: 246: 238: 227:. Retrieved 223: 214: 203:. Retrieved 199:the original 194: 168:Magic square 155: 151: 119: 115: 113: 103: 99: 97: 87: 86:, a type of 64: 60: 48: 44: 42: 24: 22: 667:mathematics 634:Magic graph 614:Word square 339:recmath.org 150:concentric 29:magic graph 714:Categories 550:Magic cube 474:Magic star 386:1906.11342 365:1801.02262 344:2017-02-12 229:2017-02-12 205:2017-02-12 174:References 162:See also 33:integers 555:classes 63:) on a 53:polygon 51:, is a 316:  289:  259:  665:This 447:Types 381:arXiv 360:arXiv 31:with 671:stub 314:ISBN 287:ISBN 257:ISBN 253:199 716:: 337:. 265:. 255:. 222:. 193:. 182:^ 75:. 43:A 23:A 702:e 695:t 688:v 677:. 432:e 425:t 418:v 389:. 383:: 368:. 362:: 347:. 322:. 295:. 232:. 208:. 156:n 152:n 138:2 134:/ 130:k 120:k 118:, 116:n 104:n 100:n 65:k 61:N 20:.

Index

Polygon Magic
magic graph
integers
polygon
magic constant
generalization
magic triangles

magic triangles
Magic square


"Perimeter Magic Polygons"
the original
"Perimeter Magic Polygon >k=3"
Math Skills: Arithmetic with Introductory Algebra and Geometry
199
ISBN
9780787292966
Even More Mathematical Activities
ISBN
9780521339940
Unsolved Problems in Geometry: Unsolved Problems in Intuitive Mathematics
ISBN
9781461209638
"Perimeter Magic Triangles"
arXiv
1801.02262
arXiv
1906.11342

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