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Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume II: Geometry
Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume II: Geometry



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Íàçâàíèå: Fundamentals of Mathematics, Volume II: Geometry

Àâòîðû: Behnke H., Bachmann F., Fladt K.

Àííîòàöèÿ:

Volume II of a unique survey of the whole field of pure mathematic


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1974

Êîëè÷åñòâî ñòðàíèö: 696

Äîáàâëåíà â êàòàëîã: 26.02.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
$T_1$-axiom      662
$\varepsilon$-covering      658
$\varepsilon$-neighborhood of a point p      638
Abelian group      11 62 619
Absolute circular point      414
Absolute conic section      414
Absolute figure      461 490
Absolute geometry      138—141 145—162
Absolute involution      413—414
Absolute polarity      413—414
Absolute simplex      611
Absolute sphere-circle      414n
Adjoint mapping      374
Adjoint representation      526
Adler, A.      228
Admissible mapping      535
Affine continuous metric plane      189
Affine geometry      180—182 297
Affine group      310—312 397 461—462
Affine line      527
Affine mapping      25 310—325 397—398
Affine plane      66—95 169 180
Affine plane, Desarguesian      182 310
Affine plane, Pappus      303—306
Affine point space      297—302
Affine reflection      316
Affine subspaces      335—345
Affine transormation      7 22
Affine-coordinate plane      85—90 114 124 300
Affinity      81—82 311—325
Affinity, algebraic description of      312—313
Affinity, axial      80—81 94 316 394
Affinity, classification of      314
Affinity, Euler      316—317
Affinity, representation of      93—95
Alexander lemma      651—652
Alexander, J.W.      631
Algebra, exterior, of Grassmann      294
Algebraic curves      438—453
Algebraic geometry      452
Algebraic surface      453—458
Algebraization, of Euclidean planes      124—127
Algebraization, of metric planes      168—173
Alternating product      360—365 486
Altitudes, of a tetrahedron      357—358
Altitudes, of a triangle      356
Altitudes, theorem of      125—126 152—153
angle      13—18 185—186 417—419
Angle, at the circumference of a circle      362
Angle, between vectors      346
Angle, bisection of      151 356—357
Angle, cosine theorem for      372
Angle, measure of      361 417n 495
Angle, of a polygon      239—242
Angle, of rotation      418
Angle, oriented      361
Angle, trisection of      230—233 235
Angle-sum      367—368 507
Annulus      598
Anti-prism      278
Antiparallel-equal      36—37
Apollonius      437
Apollonius contact problem (tangency problem)      480 485—486
Approximation, simplicial      631 665—666
Arc, cos function      347
Arc, Jordan      643—644
Arc, length      537—538 547
Arc, of a curve      640
Archimedes      233
Archimedes, axiom of      13 184—185
Archimedes, spiral of      437
Archimedes, system      13
Area      18—23
Area, of an oval      576
Area, surface      373 547—551
Asplund and Grunbaum theorem      584
Asymptote      440
Asystatic representation      525
Automorphism, group      24 460—461
Automorphism, inner      526
Automorphism, of Euclidean space      374
Axial affinity      80—81 94 316 394
Axial perspectivity      402
Axioms      11
Axioms, independence of      27—28
Axioms, model of, system      62—63
Axioms, of order      339
Axioms, system for absolute geometry      138—141 145—147
Axioms, system for affine planes      66—68
Axioms, system for Euclidean planes      113—114
Axioms, system for three-dimensional projective space      102—105
Axis, of a central collineation      393—395
Axis, of a conic section      422—424
Axis, of a pencil      148
Axis, of perspectivity      97
Axis, of reflection      378
Axis, of rotation      417
Axis, principal      380
Axis, radical      429
Banach space      349
Barycentric coordinates      344 390 665 667—668
Base points of a pencil      429
Base, ordered      340
Basis      296
Basis, conjugate      328
Basis, for a topological space      663
Basis, orthogonal      347
Basis, orthonormal      348 353 415
Bernoulli, Johann      562
Betti group      621
Betti number      621—622 631 650
Bilateral      6—7
Bilinear form      108—109 110 325—327 329 345—346 379—380
Bilinear outer product      486
Binormal      539
Birational correspondence      440
Birational equivalence of two curves      452—453
Birational transformation      438 454
Birationally related classes of surfaces      458
Blaschke's theorem      576 577—579 583—584
Bolyai, Janos      490
Boundary chain      616—617
Boundary curve      595
Boundary of a domain      648
Bounded set      639
Bounding line      573
Bourbaki, Nicolas      661
Branch of a curve      441
Breadth of a curve      574
Brianchon theorem      158—160 426
Brill, A.W.      438
Brouwer dimension theorem      654
Brouwer, L.E.J.      595 659
Brunn theorem      581
Bundle, dualization      408
Bundle, model of elliptic geometry      502—503
Bundle, of circles      473—474 484
Bundle, of cycles      479
Bundle, of Lie circles      484
Bundle, of lines      401 488
Bundle, of planes      401
Calculus of variation      559—560
Calculus, of segments (Hilbert)      90—93
Calculus, reflection      30
Calculus, vector      30
Calculus, with points      30
Canonical system of generators      62
Cantor definition of a curve      660
Cantor discontinuum      637
Carpenter's square      235—237
Carrier      148 167—168 387 401
Carrier simplex      665
Cartan, E.      533
Cartesian coordinate system      415
Cartesian product      176n
Castelnuovo, Guido      438
Cauchy theorem on polyhedra      266
Cauchy — Schwarz inequality      346
Cavalieri principle      20
Cayley, A.      107 490
Cayley-Klein geometries      490—501
Center      317 393—395
Center of a conic section      421—422
Center of a pencil      148
Center of a quadric      432
Center of curvature      540
Center of gravity      54—61 356 390 580—581
Center of perspectivity      97
Central collineation      395
Central dilation      316—317
Central line of a penicl      430
Central ovoid      580—584
Central quadric      328 381
Central-elliptic geometry      501
Central-hyperbolic geometry      501
Ceulen, von, doubling formula of      243—245
Chain      616—635
Change of direction      478 485
Chasles relation      33 55
Christoffel three-index symbols      556
circle      351 381 423 584—588
Circle, bundle of      473—474 484
Circle, inversion in a      456—457 471
Circle, Lie      466 483^84
Circle, limit      510
Circle, linear set of      473—474
Circle, measurement of      248—252
Circle, of constant geodesic distance      568
Circle, oriented      465
Circle, pencil of      429—431 473—474 484
Circular point, absolute      414
Circular transformation      469
Circumcircle of a polygon      242
Circumference of an oval      576—577
Cissoid of Diodes      437
Clebsch, R.F.A.      457
Closed chain      617—619
Closed halfspaces      343
Closed manifold      604—609
Closed path      635
Closed set      517 639
Closure      638
Closure, theorems      68—76 82—84 91—92 150—153
Cloverleaf loop      593—594
Collinear      66
Collineation      76—82 94 306—307 393—400 461
Collineation, central      395
Collineation, involutory      394
Collineation, of a projective plane      98—99
Collineation, orthogonal      132—133
Collineation, perspective      98 393
Collineation, projective      99 395—397 400—401
Combinatorial geometry      574
Combinatorial topology      595 616
Compact      647 651
Compactum      659—660
Comparativity      11 179
Compass construction      199—210 222—229
Complement      244 639
Complete quadrangle, theorem of the      388
Complete quadrilateral      107 335—336
COMPLEX      595—596 609—616
Complex geometry      391—393
Conchoid of Nicomedes      437
Cone      329 381 412 457^58 482
Congruence      298 349 375 379 512
Congruence, axioms      183—189
Congruence, class of segments      24
Congruence, invariance of an area under      22
Congruence, relation      183—189
Congruence, theorem      512
Conic section      100 325 332 412 419—431
Conic section, absolute      414
Conic section, axis of      422—424
Conic section, diameter of      421—422
Conic section, proper      381
Conic section, vertex of      423—424
Conies, as an algebraic curve      438—440
Conies, homaloidal net of      457
Conies, imaginary      421
Conies, line      496—497
Conies, nondegenerate      439
Conies, point      496—497
Conies, projective generation of      425—427
conjugate      388—389 410 421
Conjugate basis      328
Conjugate midline      590
Conjugate pair      403—405
Connected set      639
Connective relation      517
Connectivity      631—635 649—650
Constructible problems      199
Constructible regular n-gon      257—259
Construction, Mascheroni      224—229
Construction, methods of      200—201
Construction, Mohr      224—229
Construction, of classes      24
Construction, of higher degree      229—237
Construction, problems      208—209
Construction, Steiner      214—218
Construction, von Staudt's pentagon      253
Construction, with compass      224—229
Construction, with straightedge alone      210—224
Construction, with straightedge and compass      199—210
Construction, with straightedge and gauge      220—223
Contact (tangency) problem of Apollonius      485—486
Contact point      638
Continuity      180
Continuity, axiom of      178—180
Continuity, Dedekind      22
Continuity, geometry of      596
Continuity, of mappings      517
Continuous function      642
Continuous mapping      664—670
Continuous plane      143—145 180 182 189
Continuous representation      519—520
Continuously ordered set      646
Continuum      639 641 642—644
Contravariant tensor      545
Contravariant vector      545
Convex body      572
Convex hull      265—266
Convex point      572
Convex polygon      239 241—242
Convex polyhedra      265—272 343—344
Convex sets      342—345
Convexity      343—345
Coordinate      85—95
Coordinate plane      124—127 389
Coordinate plane, affine      85—90 114 124
Coordinate simplex      313
Coordinate system      313 392 415
Coordinate vector      385—387
Coordinate, affine      300
Coordinate, barycentric      344 390 665 667—668
Coordinate, geodesic polar      567
Coordinate, homogeneous      345 389—391
Coordinate, in projective space      385—393
Coordinate, line      439 487
Coordinate, normal      569
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