MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández Fig. 4 is the pseudotetrahedron by T. Yenn. At left we have the folding plan, in the center the solid ...

Mathematics and Origami of Fig. 6 (lines BH, BD, FH y FD in Fig. 8): The result is that in vertices B and F certain tensions are ...

Jesús de la Peña Hernández 17.2 VIRTUAL SURFACES Let ́s start with Fig. 9 (Point 17.1) to get Fig.1 of present Point 17.2. Thus ...

Mathematics and Origami A conoid is a ruled surface with: Its own right directrix. A director plane not parallel to it. Another ...

Jesús de la Peña Hernández Conoids are warped (not developable) ruled surfaces (with straight generatrices). One surface is deve ...

Mathematics and Origami Start with a square with base AB = a and center O (Fig. 10). Rotate it clockwise on its own plane aroun ...

Jesús de la Peña Hernández We have seen up to now that CAD allows us to draw Fig. 13 as well as Fig. 11. Then we ́ll see the ana ...

Mathematics and Origami Once we know the co-ordinates of A, B, C, D, it is easy to obtain the length of BD and AD: BD= ()( )()xD ...

Jesús de la Peña Hernández 18 POLYHEDRA They are solids bounded by plane faces (polygons, obviously in number of 4 or more). Th ...

Mathematics and Origami Irregular polyhedra do not openly conform with to equality conditions of regular polyhedra. Neither do t ...

Jesús de la Peña Hernández This construction associates geometry and paperfolding, and has these characteristics: It starts wit ...

Mathematics and Origami cial graduated squares able to configure any type of angles. That craft has even assigned specific names ...

Jesús de la Peña Hernández RELATION BETWEEN c AND d (Fig. 4) senβ a EH= ;       = − = − − 2 tg π GE EF FG e a β ; () d GE ...

Mathematics and Origami 18.2 PYRAMIDS We are going to study various regular pyramids and one irregular, using when possible, for ...

Jesús de la Peña Hernández 18.2.1.2 OF TRI-RIGHT-ANGLED VERTEX From a square of side l (Fig. 1), we get a virtual pyramid (I nam ...

Mathematics and Origami The lateral side (see Fig. 1) is: () 2 3 1 2 2 1 2 + = The pyramid ́s altitude is (Fig. 5): 2 1 2 2 ...

Jesús de la Peña Hernández Fig. 2 shows, as said, how to pleat fold, at the discretion of the folder (but with a great accuracy) ...

Mathematics and Origami 18.2.4 HEXAGONAL PYRAMID The folding process beginning in Fig. 1, is self-explanatory. Fig. 5 shows how ...

Jesús de la Peña Hernández 18.2.5 RHOMBIC PYRAMID The one to be studied now is an irregular pyramid whose base is a rhomb having ...

Mathematics and Origami 18.3 PRISMS Let us construct an oblique equilateral triangular prism whose lateral sides form with the b ...