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Birkhoff G.D., Beatley R. — Basic Geometry
Birkhoff G.D., Beatley R. — Basic Geometry



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Название: Basic Geometry

Авторы: Birkhoff G.D., Beatley R.

Аннотация:

This textbook in geometry differs in several essential respects from other current texts covering the same subject-matter. The nature of these differences is readily apparent to any experienced teacher who briefly scrutinizes the content of the book. In this connection, however, a word of caution is in order. Teachers of experience, from their very familiarity with other texts, may tend at first sight to be misled by the novelty of this presentation and may see in it a difficulty which is apparent rather than real. They should be quick to realize, however, that their students—unhampered by experience—will not be so bothered. Actual classroom experience with an experimental edition of these materials over a period of several years has conclusively demonstrated their teachability. From these materials students acquire a mastery of geometry that is noticeably superior to the mastery gained from the traditional handling of the subject. Moreover, students trained according to the principles of this book need have no fear of college entrance examinations in geometry.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third edition

Год издания: 1999

Количество страниц: 294

Добавлена в каталог: 11.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Proposition (s), opposite      246—247 249—251
Proposition (s), opposite converse      247 252
Proposition (s), original      100
Proposition (s), restricted to plane figures      5 39
Protractor      46 165—172
Pythagorean Theorem      90—98
Quadrilateral (s)      56
Radical axis      262—263
RADIUS      15 133 136
Radius of regular polygon      204
Reasoning in disputes      9—11 268
Reasoning in non-mathematical situations      9—36 161—163 268—283
Reasoning, begging the question      31 32 280
Reasoning, common errors in      29—32
Reasoning, deductive      273—277
Reasoning, necessity for logical      12
Reasoning, non-sequitur      29
Rectangle(s)      118 199 222
Rectangular network      118—123
Reductio ad absurdum      35
Refutation      35
Regular polygons      85 133—159 170—172 190—196 210—212
Regular polyhedrons      188—189 196 202 219—220
respectively      14
Rhombus      118
Right angle      50
right triangle      84 85—86 90—93
Right triangle, 30°-60°      96
Ruler      40 60 165 280
SCALE      40 60 165 280
Secant      137 151
Sector      213 225
Segment, line      44 166—170 176—178 192
Semicircle      134
Side(s) of angle      46
Side(s) of polygon      55
Similar      105
Similar figures      57
Similar polygons      57 205—206
Similar right triangles      85
Similar triangles, Case 1      58—60
Similar triangles, Case 2      72—75
Similar triangles, Case 3      78—80
Skew lines      130
slope      120—123
Solid geometry      5 39 61 75 82 101—102 129—130 160—161 188—189 196 202 206—207 215—217 219—220 243—245 250—252 260—261 263—266
Solids five regular      188—189 196 202 219—220
Square      118 199 222
Starred exercises      5 52
Straight angle      46 50
Straight line      39
Straightedge      60 165—196
summaries      67—68 98—99 130—131 156 220—221
Superposition      3
Symbols, $\angle$      21
Symbols, $\triangle$      200
Symbols, <, >      34 285
Symbols, = , +, $\times$      285
Symmetry      124—126
System of parallels      108 110 111 118
System, logical      12 35—36 106 268—270 273—274 280—283
Tangent      138 151 183—185
Tangent, circles      143
Tangent, common external      144 184—185
Tangent, common internal      144 184—185
Theorem(s)      19
Theorem(s), listed in summaries      98—99 130—131 156 220—221
Theorem(s), seven basic      71—93 107
Theorem(s), various forms of stating      22 27—29
Transversal      109—113
trapezoid      115—116 202
Triangle(s)      38 56
Triangle(s), acute      84
Triangle(s), altitude of      74
Triangle(s), area of      200—201 222
Triangle(s), base of      245
Triangle(s), can be reproduced      59
Triangle(s), centroid of      259
Triangle(s), circumcenter of      255
Triangle(s), construction of      185—188
Triangle(s), equal ("congruent")      59 80
Triangle(s), equiangular      77
Triangle(s), equilateral      77
Triangle(s), incenter of      256
Triangle(s), isosceles      75—77
Triangle(s), median of      259
Triangle(s), obtuse      84
Triangle(s), orthocenter of      259
Triangle(s), right      84 85—86 90—93 96
Triangle(s), similar, Case 1      58—60
Triangle(s), similar, Case 2      72—75
Triangle(s), similar, Case 3      78—80
Triangle(s), spherical      61 75 82
Triangle(s), sum of angles of      82—85
Triangle(s), sum of two sides of      94
Triangle(s), the vertex of a      245
Trisection of an angle      166 171 189—190 195
Truth      18 19 23 29 277—278
Truth of converse      26 27
Undefined terms      12 13 17 25 38 39 280—283
Undefined terms, list of      39 281 285
Unit of angle measure      46 49—50 52—53
Unit of area      199 222
Unit of length      40—42 199
Vertex, vertices of a polygon      55
Vertex, vertices of a triangle      245
Vertex, vertices of angle      46
Vertical angle      52
Volume      206—207 216—217
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