Fractal Geometry and Applications: A Jubilee of Benoit - download pdf or read online

By Lapidus M., van Frankenhuijsen M. (eds.)

ISBN-10: 0821836374

ISBN-13: 9780821836378

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Extra resources for Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot, Part 1

Example text

1/7 The intersection at the dot divides the square into 3/7 and 4/7. Fold and unfold. The 1/7 mark. Divisions of 1/8 The standard method for finding the 1/8 mark is to divide the paper in half three times. That would take three folds. This clever method requires only two folds. 1 2 3 4 3/8 1/8 Fold and unfold at the top. 26 Fold on the left. Part I: Designing Origami Polyhedra 1/8 Unfold. The 3/8 mark is also found. The 1/8 mark. Divisions of 1/9 This is an example of the edge method for dividing the square into n2 parts as shown on page 30.

4 7 Unfold. 8 Fold and unfold creasing lightly. 9 10 Crease on the left. 11 12 Unfold. 13 14 15 Unfold. 16 Heptagon Heptagon 55 Octagon Some polyhedra have octagonal sides, including an octagonal pyramid and antiprism. 414236 ≈ 1+ 2 The angle at each vertex = 135°. Let the length of each side = 1. 414236 = 1 + 2. Folding method: 1 2 Fold and unfold by the corners. 3 Crease on the left. 4 5 Unfold and rotate 90°. 7 6 Repeat steps 2−4 three more times. Refold.

Find c. 5 d c Design Method Examples 43 4. Find e. 1464466 = (2 − 2) 4 α α f e 5. Find g, first find k. 2679491 = tan(15°). 2679491 = tan(15°) Of these, a and g are easy to find and sufficient for completing the folding pattern. 5°). 2679491 = tan(15°). 44 Part I: Designing Origami Polyhedra 1 2 15° Fold and unfold. 2679491 = tan(15°) Polygons Since polygons are the faces of polyhedra, we present how to fold certain polygons before we move into folding directions for polyhedra. Many of the polyhedra in this collection have faces that are regular polygons, which are polygons with congruent angles and sides.

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Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot, Part 1 by Lapidus M., van Frankenhuijsen M. (eds.)

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