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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

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2006

Количество страниц: 152

Добавлена в каталог: 07.04.2008

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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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