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Walser H., Pedersen J. — 99 Points of Intersection: Examples, Pictures, Proofs
Walser H., Pedersen J. — 99 Points of Intersection: Examples, Pictures, Proofs

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Название: 99 Points of Intersection: Examples, Pictures, Proofs

Авторы: Walser H., Pedersen J.

Аннотация:

The 99 points of intersection presented here were collected during a year-long search for surprising concurrence of lines. For each example we find compelling evidence for the sometimes startling fact that in a geometric figure three straight lines, or sometimes circles, pass through one and the same point. Of course, we are familiar with some examples of this from basic elementary geometry - the intersection of medians, altitudes, angle bisectors, and perpendicular bisectors of sides of a triangle. Here there are many more examples - some for figures other than triangles, some where even more than three straight lines pass through a common point.

The main part of the book presents 99 points of intersection purely visually. They are developed in a sequence of figures, many without caption or verbal commentary. In addition the book contains general thoughts on and examples of the points of intersection, as well as some typical methods of proving their existence. Many of the examples shown in the book were inspired by questions and suggestions made by students and high-school teachers. Several of those examples have not only a geometrical, but also an intriguing aesthetic, aspect.

The book addresses high-school students and students at the undergraduate level as well as their teachers, but will appeal to anyone interested in geometry


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 152

Добавлена в каталог: 07.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
12-gon      1
16-gon      20
18-gon      21 22 23 24 25 26
Affine image      122
Affine invariance      122 126
Affine regular      141
Angle version      129
Arbelos      50
Butterflies      107
Calculation      119
Cartesian representation      7
Center of gravity      17 117 125 127 136
Center of the circumcircle      117 122
Center of the incircle      117 122
Central projection      122
Centroid      117 118 123
Ceva's theorem      125 126 127 129 144
Ceva, Giovanni      125
chebyshev      10
Chebyshev polynomial      10 11
Chord      4
circle      4 5 54 62
Circle of Apollonius      15
Circle-reflection      4
Circuit      69 123
circumcircle      5 37 42 43 44 137 146
Cloverleaf      51
Common tangents      63
complex numbers      140
Computer-Algebra System      121 140
cube      62 76
Desargues, Girard      99
Diagonal      2 4 8 19 20 21 22 23 24 25 26
Dialogue      118
DIN-Format      29 30
Dodecagon      1 4 18 19
Dynamic Geometry Software      121
ellipse      28
Equilateral triangle      4 7
Euler line      117
Fermat-point      136
Feuerbach, Karl      104
Flower      6 7 8
FOURIER      6
FOURIER-expansion      7
Ghost circle      14
Ghostly curve      12
Golden section      11 12
Great circle      131
Hexagon      141
Homogeneous coordinates      140
Homothetic      122
Hyperbola      135 136
Hyperbolic geometry      4
incidence      122
incircle      38 39 124 138
Intersection of altitudes      128
Isosceles triangle      4
Jacobi's theorem      132 135
Kiepert's hyperbola      135
Kissing circles      102
Klein model      4
Kroll, Wolfgang      32 35 40 41 69 123
Law of Cosines      141
Lissajous curve      11 12 13
Macbeth      118
Malfatti, Gian Francesco      45
midpoint      17
Mirror-image      17 42 43
n-gon      130
Non-Euclidean      4
Oblique diagonal      2
Optical effect      12
Orthogonal      4
parabola      12
Parallelism      122
Perspective similarity      122
Perspectively similar triangles      124
Petal      6
Poincare model      4
Polar coordinates      8
propeller      96
Puzzle      4
Pythagoras      80 82 128 141
Recurrence relation      10
Regular hexagon      115 145
Regular n-gon      145
Regular pentagon      111 114
Shakespeare      118
Spherical geometry      131
Spherical triangles      131
Spirit      10
Square      4 112
Star of David      33 34
Subdivision-puzzle      4
Symmetry      2 17
Thales      31
Vanishing point      1
Vector geometry      119
Vertex      3
Wyss, Roland      93
Zigzag      27
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