MATHEMATICS AND ORIGAMI

(Dana P.) #1
III

9.18 Division of a paper strip by means of binomial numeration....................................... 98


10 Regular convex polygons with more than 4 sides ...................................................... 102


10.1 Pentagon ...................................................................................................................... 102
From an argentic rectangle. From a DIN A 4. From a paper strip
made out of argentic rectangles. With a previous folding. Knot
type..


10.2 Hexagon ....................................................................................................................... 108
With a previous folding. Knot type.


10.3 Heptagon ...................................................................................................................... 109
H. Huzita ́s solution. A quasi-perfect solution. Knot type solution.


10.4 Octagon ........................................................................................................................ 113


10.5 Enneagon ..................................................................................................................... 114


11 Stellate polygons .......................................................................................................... 11 6
Pentagon (S. Fujimoto) and Heptagon. Flattening conditions.
Hexagonal star (4 versions)


12 Tessellations ................................................................................................................ 123
By Forcher, Penrose, Chris K. Palmer, Alex Bateman and P.
Taborda.
13 Conics .......................................................................................................................... 131
13.1 Circumference: Its center. As the envelope of its own tangents
(inscribed within a square, or concentric with another one)
13.2 Origami and plückerian coordinates ............................................................................ 133


13.3 Ellipse .......................................................................................................................... 136
Its parameters. As envelope of its own tangents. Directrix. Poles
and polars. Inscribed within a rectangle. Poncelet ́s theorem.


13.4 Parabola ....................................................................................................................... 143


13.5 Hyperbola..................................................................................................................... 144


13.6 Another curves ............................................................................................................. 145
Logarithmic spiral. Cardioid. Nephroid.


14 Topologic evocations ................................................................................................... 150


14.1 Möbius ́ bands.............................................................................................................. 150


14.2 Flexagons ..................................................................................................................... 152


15 From the 2nd to the 3rd dimension ................................................................................ 156

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