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Negative pedal curve

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For a parametrically defined curve, its negative pedal curve with pedal point (0; 0) is defined as
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Unsourced material may be challenged and 579: 565: 557: 440: 427: 417: 394: 309: 296: 286: 263: 117:Learn how and when to remove this message 7: 51:adding citations to reliable sources 14: 552:Negative pedal curve on Mathworld 175:, the negative pedal curve has a 23: 215:there is a unique line through 649:Pedal & Contrapedal curves 525:The negative pedal curve of a 446: 420: 411: 399: 315: 289: 280: 268: 207:In the plane, for every point 163:on that curve. For each point 1: 136:— negative pedal curve of a 587:Differential transforms of 768: 247:lies on the given curve. 16:Mathematical plane curve 511: 380: 140: 66:"Negative pedal curve" 752:Differential geometry 719:on a family of curves 676:defined by two points 512: 381: 132: 654:Negative pedal curve 393: 262: 233:negative pedal curve 179:that passes through 149:negative pedal curve 47:improve this article 695:defined by a point 642:defined by a point 507: 376: 195:to constructing a 159:and a fixed point 141: 734: 733: 693:Binary operations 505: 374: 219:perpendicular to 193:inverse operation 127: 126: 119: 101: 759: 674:Unary operations 640:Unary operations 597:Unary operations 581: 574: 567: 558: 516: 514: 513: 508: 506: 504: 503: 489: 477: 476: 456: 445: 444: 432: 431: 418: 385: 383: 382: 377: 375: 373: 372: 358: 346: 345: 325: 314: 313: 301: 300: 287: 251:Parameterization 122: 115: 111: 108: 102: 100: 59: 27: 19: 767: 766: 762: 761: 760: 758: 757: 756: 737: 736: 735: 730: 711: 687: 668: 634: 591: 585: 548: 535: 523: 496: 482: 478: 469: 449: 436: 423: 419: 391: 390: 365: 351: 347: 338: 318: 305: 292: 288: 260: 259: 253: 205: 123: 112: 106: 103: 60: 58: 44: 28: 17: 12: 11: 5: 765: 763: 755: 754: 749: 739: 738: 732: 731: 729: 728: 722: 720: 713: 712: 710: 709: 704: 698: 696: 689: 688: 686: 685: 679: 677: 670: 669: 667: 666: 661: 656: 651: 645: 643: 636: 635: 633: 632: 627: 625:Parallel curve 622: 617: 612: 607: 601: 599: 593: 592: 586: 584: 583: 576: 569: 561: 555: 554: 547: 546:External links 544: 543: 542: 534: 531: 522: 519: 518: 517: 502: 499: 495: 492: 488: 485: 481: 475: 472: 468: 465: 462: 459: 455: 452: 448: 443: 439: 435: 430: 426: 422: 416: 413: 410: 407: 404: 401: 398: 387: 386: 371: 368: 364: 361: 357: 354: 350: 344: 341: 337: 334: 331: 328: 324: 321: 317: 312: 308: 304: 299: 295: 291: 285: 282: 279: 276: 273: 270: 267: 252: 249: 204: 201: 125: 124: 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 764: 753: 750: 748: 745: 744: 742: 727: 724: 723: 721: 718: 714: 708: 705: 703: 700: 699: 697: 694: 690: 684: 681: 680: 678: 675: 671: 665: 662: 660: 659:Pursuit curve 657: 655: 652: 650: 647: 646: 644: 641: 637: 631: 628: 626: 623: 621: 620:Inverse curve 618: 616: 613: 611: 608: 606: 603: 602: 600: 598: 594: 590: 582: 577: 575: 570: 568: 563: 562: 559: 553: 550: 549: 545: 540: 537: 536: 532: 530: 528: 520: 500: 497: 493: 490: 486: 483: 479: 473: 470: 466: 463: 460: 457: 453: 450: 441: 437: 433: 428: 424: 414: 408: 405: 402: 396: 389: 388: 369: 366: 362: 359: 355: 352: 348: 342: 339: 335: 332: 329: 326: 322: 319: 310: 306: 302: 297: 293: 283: 277: 274: 271: 265: 258: 257: 256: 250: 248: 246: 242: 239:of the lines 238: 234: 230: 227:, called the 226: 222: 218: 214: 210: 202: 200: 198: 194: 190: 186: 185:perpendicular 182: 178: 174: 171:on the curve 170: 167: ≠  166: 162: 158: 154: 150: 146: 139: 135: 131: 121: 118: 110: 99: 96: 92: 89: 85: 82: 78: 75: 71: 68: –  67: 63: 62:Find sources: 56: 52: 48: 42: 41: 37: 32:This article 30: 26: 21: 20: 653: 589:plane curves 524: 254: 244: 240: 232: 228: 224: 220: 216: 212: 208: 206: 188: 180: 172: 168: 164: 160: 156: 148: 142: 113: 104: 94: 87: 80: 73: 61: 45:Please help 33: 527:pedal curve 229:pedal point 211:other than 197:pedal curve 153:plane curve 741:Categories 717:Operations 615:Dual curve 539:Fish curve 521:Properties 243:for which 203:Definition 77:newspapers 683:Strophoid 491:− 434:− 360:− 303:− 107:June 2012 34:does not 726:Envelope 702:Roulette 610:Involute 533:See also 501:′ 487:′ 474:′ 454:′ 370:′ 356:′ 343:′ 323:′ 237:envelope 187:to line 145:geometry 707:Cissoid 664:Caustic 630:Isoptic 605:Evolute 235:is the 183:and is 177:tangent 138:limaçon 91:scholar 55:removed 40:sources 747:Curves 231:, the 134:Circle 93:  86:  79:  72:  64:  151:is a 98:JSTOR 84:books 147:, a 70:news 38:any 36:cite 143:In 49:by 743:: 241:XP 221:XP 199:. 189:XP 580:e 573:t 566:v 498:x 494:y 484:y 480:x 471:y 467:y 464:x 461:2 458:+ 451:x 447:) 442:2 438:y 429:2 425:x 421:( 415:= 412:] 409:y 406:, 403:x 400:[ 397:Y 367:x 363:y 353:y 349:x 340:x 336:y 333:x 330:2 327:+ 320:y 316:) 311:2 307:x 298:2 294:y 290:( 284:= 281:] 278:y 275:, 272:x 269:[ 266:X 245:X 225:P 217:X 213:P 209:X 181:X 173:C 169:P 165:X 161:P 157:C 120:) 114:( 109:) 105:( 95:· 88:· 81:· 74:· 57:. 43:.

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Circle
limaçon
geometry
plane curve
tangent
perpendicular
inverse operation
pedal curve
envelope
pedal curve
Fish curve
Negative pedal curve on Mathworld
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