Knowledge (XXG)

99 Points of Intersection

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170:. The second section shows the 99 points of intersection of the title. Each is given on its own page, as a large figure with three smaller figures showing its construction, with a one-line caption but no explanatory text. The third section provides background material and proofs for some of these points of intersection, as well as extending and generalizing some of these results. 229:
John Jensen writes that "the clear and uncluttered illustrations of intersection make for a rich source for geometric investigation by high school geometry students". And although Gerry Leversha calls the book "eccentric" and states that it "is clearly nothing to do with any syllabus anywhere",
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The book is organized into three sections. The first section provides introductory material, describing different mathematical situations in which multiple curves might meet, and providing different possible explanations for this phenomenon, including symmetry, geometric transformations, and
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and in a geometry course focused on the formal proof of geometry propositions. He adds that the book itself is a proof of the possibility of presenting geometry without detailed explanations, and of introducing students to the beauty of the subject.
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in which three or more lines or curves meet in a single point of intersection. This book was originally written in German by Hans Walser as
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Jensen suggests that its examples would make a good complement to coursework both in exploratory geometry using
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Some of these points of intersection are standard; for instance, these include the construction of the
218: 167: 253: 214: 190: 407: 372: 364: 202: 182: 150: 425: 356: 206: 26: 210: 464: 376: 142: 66: 194: 138: 61: 454: 186: 360: 457:, web site with a larger collection of points of intersection, by Hans Walser 205:. However, others are new to this book, and include intersections related to 178: 174: 411: 368: 137:(Eagle / Ed. am Gutenbergplatz, 2004), translated into English by 124:
99 Points of Intersection: Examples—Pictures—Proofs
110: 91: 83: 75: 54: 44: 36: 201:of the sides meet, as well as two versions of 8: 343:Leversha, Gerry (November 2008), "Review of 19: 25: 18: 244: 394:Jensen, John (March 2007), "Review of 149:in 2006 in their MAA Spectrum series ( 389: 387: 385: 338: 336: 334: 332: 304: 302: 300: 282:Poplicher, Mihaela (September 2006), 277: 275: 273: 271: 7: 185:lines meet, the construction of the 319:Journal of Recreational Mathematics 147:Mathematical Association of America 102:Mathematical Association of America 193:meet, and the construction of the 14: 309:Ashbacher, Charles (2004–2005), 434:Australian Mathematics Teacher 166:membership of the curves in a 127:is a book on constructions in 1: 232:interactive geometry software 197:as the point where the three 189:as the point where the three 181:as the point where its three 98:Eagle / Ed. am Gutenbergplatz 263:German Mathematical Society 502: 20:99 Points of Intersection 428:99 Points of Intersection 396:99 Points of Intersection 361:10.1017/S0025557200184074 345:99 Points of Intersection 313:99 Points of Intersection 286:99 Points of Intersection 24: 471:Euclidean plane geometry 349:The Mathematical Gazette 129:Euclidean plane geometry 87:Euclidean plane geometry 424:Coupland, Mary (2006), 400:The Mathematics Teacher 199:perpendicular bisectors 161:Topics and organization 145:, and published by the 486:2006 non-fiction books 481:2004 non-fiction books 31:First edition (German) 219:nine-point hyperbola 215:Pythagorean theorem 45:Original title 21: 16:2004 geometry book 476:Mathematics books 207:silver rectangles 155:978-0-88385-553-9 120: 119: 493: 442: 441: 421: 415: 414: 391: 380: 379: 355:(525): 588–589, 340: 327: 326: 306: 295: 294: 279: 266: 265: 257:99 Schnittpunkte 249: 168:pencil of curves 134:99 Schnittpunkte 112:Publication date 49:99 Schnittpunkte 29: 22: 501: 500: 496: 495: 494: 492: 491: 490: 461: 460: 451: 446: 445: 423: 422: 418: 393: 392: 383: 342: 341: 330: 308: 307: 298: 281: 280: 269: 251: 250: 246: 241: 227: 211:tangent circles 163: 113: 106: 71: 32: 17: 12: 11: 5: 499: 497: 489: 488: 483: 478: 473: 463: 462: 459: 458: 450: 449:External links 447: 444: 443: 416: 406:(7): 511–512, 381: 328: 296: 267: 252:Werner, Dirk, 243: 242: 240: 237: 226: 223: 203:Ceva's theorem 162: 159: 118: 117: 114: 111: 108: 107: 105: 104: 99: 95: 93: 89: 88: 85: 81: 80: 77: 73: 72: 70: 69: 64: 58: 56: 52: 51: 46: 42: 41: 38: 34: 33: 30: 15: 13: 10: 9: 6: 4: 3: 2: 498: 487: 484: 482: 479: 477: 474: 472: 469: 468: 466: 456: 455:Schnittpunkte 453: 452: 448: 439: 435: 431: 429: 420: 417: 413: 409: 405: 401: 397: 390: 388: 386: 382: 378: 374: 370: 366: 362: 358: 354: 350: 346: 339: 337: 335: 333: 329: 324: 320: 316: 314: 305: 303: 301: 297: 293: 289: 287: 278: 276: 274: 272: 268: 264: 261:(in German), 260: 259: 256: 248: 245: 238: 236: 233: 224: 222: 220: 216: 212: 208: 204: 200: 196: 192: 188: 184: 180: 176: 171: 169: 160: 158: 156: 152: 148: 144: 143:Jean Pedersen 140: 136: 135: 130: 126: 125: 115: 109: 103: 100: 97: 96: 94: 90: 86: 82: 78: 74: 68: 67:Jean Pedersen 65: 63: 60: 59: 57: 53: 50: 47: 43: 39: 35: 28: 23: 437: 433: 427: 419: 403: 399: 395: 352: 348: 344: 325:(3): 215–216 322: 318: 312: 291: 285: 258: 254: 247: 228: 195:circumcenter 172: 164: 139:Peter Hilton 133: 132: 123: 122: 121: 62:Peter Hilton 48: 426:"Review of 311:"Review of 292:MAA Reviews 284:"Review of 187:orthocenter 55:Translators 40:Hans Walser 465:Categories 255:Review of 239:References 217:, and the 116:2004, 2006 377:185487968 191:altitudes 92:Publisher 412:27972312 369:27821873 225:Audience 179:triangle 175:centroid 76:Language 440:(3): 32 84:Subject 410:  375:  367:  213:, the 183:median 153:  79:German 37:Author 408:JSTOR 373:S2CID 365:JSTOR 177:of a 151:ISBN 141:and 404:100 398:", 357:doi 347:", 157:). 467:: 438:62 436:, 432:, 402:, 384:^ 371:, 363:, 353:92 351:, 331:^ 323:33 321:, 317:, 299:^ 290:, 270:^ 221:. 209:, 430:" 359:: 315:" 288:"

Index


Peter Hilton
Jean Pedersen
Mathematical Association of America
Euclidean plane geometry
Peter Hilton
Jean Pedersen
Mathematical Association of America
ISBN
978-0-88385-553-9
pencil of curves
centroid
triangle
median
orthocenter
altitudes
circumcenter
perpendicular bisectors
Ceva's theorem
silver rectangles
tangent circles
Pythagorean theorem
nine-point hyperbola
interactive geometry software
Review of 99 Schnittpunkte
German Mathematical Society



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