Continuous Symmetry: From Euclid to KleinAmerican Mathematical Soc. - 546 من الصفحات "This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises."--BOOK JACKET. |
المحتوى
XXXVI | 235 |
XXXVII | 240 |
XXXVIII | 251 |
XL | 256 |
XLI | 266 |
XLII | 276 |
XLIII | 287 |
XLIV | 292 |
XIII | 62 |
XIV | 70 |
XV | 84 |
XVI | 94 |
XVII | 110 |
XVIII | 115 |
XIX | 119 |
XX | 121 |
XXI | 135 |
XXII | 146 |
XXIII | 156 |
XXIV | 161 |
XXV | 165 |
XXVII | 181 |
XXVIII | 188 |
XXIX | 191 |
XXX | 199 |
XXXI | 206 |
XXXII | 211 |
XXXIII | 217 |
XXXIV | 224 |
XXXV | 231 |
XLV | 298 |
XLVI | 309 |
XLVII | 315 |
XLVIII | 322 |
XLIX | 340 |
L | 347 |
LII | 356 |
LIII | 363 |
LIV | 375 |
LV | 376 |
LVI | 399 |
LVII | 416 |
LVIII | 439 |
LIX | 459 |
LXI | 467 |
LXII | 482 |
LXIII | 487 |
LXIV | 505 |
LXV | 520 |
| 531 | |
| 533 | |
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عبارات ومصطلحات مألوفة
AABC ABCD Axiom circle collinear composition compute congruent conjugacy conjugacy classes conjugate consider containing coordinate system define Definition denote desired dilation factor directed angle measure distance Dp,s equal equilateral equivalent Euclidean geometry example Exercise exists finite fixed point frieze groups frieze pattern glide reflection group G Hence Hint integer interior angles intersect invariant isometry group L-Jordan measurable l₁ lattice line segment maps medial triangle midpoint non-split non-trivial orientation-preserving orientation-reversing orthic triangle parallel lines Parallel Postulate parallelogram perpendicular bisector point group point inversion polygonal regions preserves proof properties Proposition Prove quadrilateral radius real number rectangle result rhombic rotation angle shown in Figure side length split groups square Structure Theorem Suppose symmetry group transformations translation group translation orbit translation subgroup triangle ABC uniform dilation unique verify vertex vertices wallpaper groups y₁
مقاطع مشهورة
الصفحة xiii - That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
الصفحة 4 - the best way to explain it is to do it." (And, as you might like to try the thing yourself some winter day, I will tell you how the Dodo managed it.) First it marked out a race-course, in a sort of circle, ("the exact shape doesn't matter," it said,) and then all the party were placed along the course, here and there. There was no "One, two...