MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández 18.5.1 TRIANGULAR PRISMOID Fig. 1 is a right prism whose bases are equilateral triangles. Fig. 2 is i ...

Mathematics and Origami This means that to fold flat an equilateral-triangle prismoid it is a must that the angles formed by a b ...

Jesús de la Peña Hernández This indicates that RB, in Fig. 2, is the cube ́s diagonal. From the center of the cube to its 8 vert ...

Mathematics and Origami A variant of Fig. 4 is Fig. 8 that in turn produces Fig. 9. It is not docile but it is collapsible to a ...

Jesús de la Peña Hernández The orientation of segments gp and their folding mode (mountain or valley) are sym- metric to those s ...

Mathematics and Origami 18.6 REGULAR POLYHEDRA Before digging out about them, we shall analyse certain RELATIONS given within th ...

Jesús de la Peña Hernández Fig. 4 will allow us to find the dihedral angle ε formed by two adjacent faces of a do- decahedron, a ...

Mathematics and Origami the value of VV which is the dodecahedron ́s diameter; its mid-point O is, obvi- ously, the polyhedron ...

Jesús de la Peña Hernández l l l HF 0 , 16245991 0 , 8506508 2 (^322) 2  − =       hence, the icosahedron radius will be ...

Mathematics and Origami As Ang. EBC = 108, it is: Ang. ABC = 72 ; 180 – Ang. EBC = 72 Therefore, angles ABC and EBC are suppleme ...

Jesús de la Peña Hernández 18.7 TETRAHEDRON C = 4 ; V = 4 ; A = 6 Pyramidal TETRAHEDRON Fig. 1 is the same obtained in Point 18. ...

Mathematics and Origami Skeletonlike TETRAHEDRON It is made out of 4 corners as vertices (Fig. 5) and 6 cardboard rails as sides ...

Jesús de la Peña Hernández 18.8.2 The CUBE of the sum of two numbers We know that the square of a binomial r + s (Fig. 1) is (se ...

Mathematics and Origami Figs. 7 to 8 show how the assembly is completed. 18.8.3 Magic CUBE, by Jeremy Shafer. In my opinion, thi ...

Jesús de la Peña Hernández cube as well as a beautiful illumination effect. The process simplicity is evident from the fold- ing ...

Mathematics and Origami Fig. 2 is the result of folding Fig. 1. In Fig. 1 we can see the relation between sides L and l as well ...

Jesús de la Peña Hernández Once Fig. 3 is folded we get a solid similar to that of Fig. 2; this is shown in Fig. 4 gather- ing ...

Mathematics and Origami That Fig. 4 gives: b^2 =ac ; c^2 =bd b^4 =a^2 bd ; b^3 =a^2 d= 2 a^3 ; 2 3  =      a b ; =^32 = 1 ...

Jesús de la Peña Hernández Fig. 1 also shows both parabolas with their foci and directrices respectively equidistant from the co ...

Mathematics and Origami If x is the side of the smaller cube, the imposed condition will be expressed: x^3 +()( )( )x+ 13 + x+ 2 ...