The Golden SectionThe Golden Section has played a part since antiquity in many parts of geometry, architecture, music, art and philosophy. However, it also appears in the newer domains of technology and fractals. In this way, the Golden Section is no isolated phenomenon but rather, in many cases. the first and also the simplest non-trivial example in the context of generalisations leading to further developments. It is the purpose of this book, on the one hand, to describe examples of the Golden Section, and on the other, to show some paths to further extensions. The treatment is informal and the text is enriched by the presence of very illuminating diagrams. Questions are posed at fairly frequent intervals and the answers to these questions, perhaps only in the form of very broad hints for their solution, are gathered together at the end of the text. |
Contents
Section 1 | 14 |
Section 2 | 15 |
Section 3 | 16 |
Section 4 | 17 |
Section 5 | 38 |
Section 6 | 47 |
Section 7 | 52 |
Section 8 | 60 |
Section 9 | 111 |
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Common terms and phrases
A4 paper acute Golden an+1 arises braided model c₁ cathetus center-line circle color construction diagonals dismantling step edges ellipse equilateral triangles Euclidean Algorithm example factor f Fibonacci numbers Fibonacci sequence Figure 26 Figure 78 folding follows fractal of Figure ƒ³ geometric sequences Golden Number System Golden Ratio Golden Rectangle Golden Rhombi Golden Rhombohedra Golden Section Golden Square fractal Golden Tree Golden Triangle hypercube initial values a₁ inscribed isosceles Jean Pedersen lattice linear Martin Gardner Mathematical obtain obtuse Golden obtuse rhombohedron octahedron original rectangle P(A wins parallelepiped Peter Hilton points of intersection positive solution procedure pyramids quadratic equation Question recurrence relation An+2 reduction factor regular decagon regular pentagon rhombic dodecahedron rhombic icosahedron rhombic solid rhombic triacontahedron rhombohedron right triangle satisfy the recurrence segment spiral square of side-length subdivision symmetry tree fractal Triangle fractal triangles Figure triangular vertex vertices width zigzag strips
References to this book
Essentials of Mathematics: Introduction to Theory, Proof, and the ... Margie Hale No preview available - 2003 |
Essentials of Mathematics: Introduction to Theory, Proof, and the ... Margie Hale No preview available - 2003 |