MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández Vertex ρω i – 1      − 6 cos^2 i π a () 6 1 4 π i− + i      − 6 cos^1 i π a () 6 4 π i+ S ...

Mathematics and Origami OG → OG ; E → E Result: EF OI → OI ; F → F Result: FH 13.6.2 CARDIOD A BIT OF HISTORY Fig. 1 shows the ...

Jesús de la Peña Hernández 1 → 2 2 → 4 4 → 8 8 → 16 Once we reach maximum point 16, subtract 16 (one circumference) and join to ...

Mathematics and Origami We overlap now Fig. 3 to the figure just obtained, in order to check how the rounded extremities of the ...

Jesús de la Peña Hernández 14 TOPOLOGIC EVOCATIONS If we think of topology as the science of surfaces continuity, we are taken t ...

Mathematics and Origami Glue B / B; one twist; one cut. Result (Fig. 5): band ́s length double than the original and half width ...

Jesús de la Peña Hernández Glue B / B; three twists; three cuts. Result: two independent bands, both with a length dou- ble tha ...

Mathematics and Origami One can understand why we said earlier that a flexagon is alike a Möbius band: looking afterwards how it ...

Jesús de la Peña Hernández two faces 3. What is peculiar now, though, is that the two faces 1 are different to each other, and t ...

Mathematics and Origami a rather elaborate graphical process to enable the adequate folding of a given strip. For the moment we ...

Jesús de la Peña Hernández 15 FROM THE 2nd TO THE 3rd DIMENSION Everything seen up to now has a bidimensional treatment, though ...

Mathematics and Origami Another manner to indicate the revolving angle, is to denote on the folding line the value of the dihedr ...

Jesús de la Peña Hernández We must clarify two things: a) Mountain or valley folds in Figs. 16, 17 and 18 not al- ways are in co ...

Mathematics and Origami In Fig. 18 one can see how the polyhedron angle O (DBAE) can be revolved about its base DOE from the sit ...

Jesús de la Peña Hernández ration of the α angles adjacent to the sides of the triangle and for the corresponding triset of para ...

Mathematics and Origami It is not the first time that scissors are mentioned in this book. Now, though, we are going to use a cu ...

Jesús de la Peña Hernández Fig. 34 is the simplest we can imagine; and most fascinating. Fig. 35 is the only example among the l ...

Mathematics and Origami Fig. 2 is the same Fig.1 transformed by revolving the latter about OX a dihedral angle of α = 40º (corre ...

Jesús de la Peña Hernández Fig. 3 is Fig.1 splitted out by translation, in two half-figures. In Fig. 4 those half-figures appear ...

Mathematics and Origami 17 PAPER SURFACES First of all let ́s recall how plane curves may be represented in two different manner ...