MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández Penrose has also designed another tessellation based as well on the argentic rectangle. It is compose ...

Mathematics and Origami 10 Interlude ...

Jesús de la Peña Hernández CASE 2A: Tessellation by Chris K. Palmer. Fig. 1 is a tracery among the many and very beautiful devel ...

Mathematics and Origami Fig. 6 is a tessellation based on Fig.4 showing the 5 tesserae that are produced when fitting four Figs. ...

Jesús de la Peña Hernández Between rigid Figs. 1 and 2 exists a continuous range of elastic configurations like the last shown. ...

Mathematics and Origami 13 CONICS As it ́s well known, they are curves determinated by the intersection of a cone and a plane no ...

Jesús de la Peña Hernández 13.1.2 A CIRCUMFERENCE AS THE ENVELOPE OF ITS OWN TANGENTS INSCRIBED WITHIN A SQUARE Follow the proce ...

Mathematics and Origami ference. It is pertinent to recall Point 11 about stellate polygons and Point 9.1 on how to divide a cir ...

Jesús de la Peña Hernández OP ON 1 =− (2) In same Fig. 2 we see: (^) OP=xcosβ+ycosα (3) As also it is: ON u cosβ= ; ON v cosα= ( ...

Mathematics and Origami Circumference tangential equation:^222 1 r u +v = (6) ,, Cartesian ,, ,, x^2 +y^2 =r^2 In Fig. 4 we can ...

Jesús de la Peña Hernández 13.3 ELLIPSE 13.3.1 TO FIND ITS PARAMETERS Let loose ellipse e on paper p; it may be a CAD print. Fol ...

Mathematics and Origami It means that any other point on AB but T, does not fulfil the condition of being on the ellipse. Hence ...

Jesús de la Peña Hernández Under these circumstances, any line through P 1 intersecting its polar and the ellipse produces a set ...

Mathematics and Origami To prove it we must consider the ellipse ́s peculiar equation that relates the radius vec- tors and the ...

Jesús de la Peña Hernández 13.3.3 ELLIPSE INSCRIBED WITHIN A RECTANGLE Let ́s recall first the generation of a conic by means of ...

Mathematics and Origami 13.3.4 ELLIPSE: PONCELET THEOREM. This theorem is applicable to all of three conics, but here we shall p ...

Jesús de la Peña Hernández New point G lies on T after flattening because: C → F (symmetry about tangent on T ́; Fig.1 Point 13 ...

Mathematics and Origami 13.4 PARABOLA Although we already dealt with the parabola in Points 1.2.5 and 4 now we shall insist in i ...

Jesús de la Peña Hernández 13.5 HYPERBOLA This conic is the locus of the points such that the difference of the distances from t ...

Mathematics and Origami 13.6 ANOTHER CURVES Origami deals with conics as the envelopes of their tangents; likewise we shall stud ...