MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández 9.14 DIVISION OF A SQUARE IN 7 EQUAL PARTS (two approximate solutions) Solution 1 Besides, the seven ...

Mathematics and Origami Solution 2 Beginning as usual, with a square of side 1, let ́s see how much precision we get: it is supp ...

Jesús de la Peña Hernández 9.15 A SQUARE IN 9 EQUAL PARTS (two solutions) An approximate solution It is based in the assumption ...

Mathematics and Origami 0. 1252249 ≠ 0. 122228 ≠ 0. 124226 = 0. 124226 Of course, to fold horizontally the given square through ...

Jesús de la Peña Hernández Then, the square is folded like in figs 1 and 2 (these operations are not shown in fig 3) to get 19 ...

Mathematics and Origami Fold 5 to get 7 2 a= which in turn produces 7 1 Copy and rotate 5 to get 6 which shows 7 1 x= That ...

Jesús de la Peña Hernández In 4 appears 12 2 6 1 a= =. In said square 4 fold its right lower vertex to lie on the upper side, ...

Mathematics and Origami 20 2 10 1 = 19 1 38 2 19 1 = 37 1 All this proves the need to do first the re- verse way to get the conf ...

Jesús de la Peña Hernández 9.17 DIVISION OF A PAPER STRIP (Fujimoto ́s method) It deals with a system of successive approximatio ...

Mathematics and Origami Fold A over D to get C ́: () () 4 4 1 2 1 4 1 2 1 2 2 1 1 2 1 2 ́ ́ x x x AD BD AC CD = − + − = − − − = ...

Jesús de la Peña Hernández Being n the number of folds, and generalising, we have: 2 3 Limx n nx 2 3 2 1 2 1 = − + Lim 3 1 2 1 3 ...

Mathematics and Origami AC x 256 1 256 1 64 1 16 1 4 1 ́ ́= − + − + The latter expression gives us the formation law of AC j tha ...

Jesús de la Peña Hernández 9.18 DIVISION OF A PAPER STRIP BY MEANS OF BINOMIAL NUMERATION As we know, in binary numeration the o ...

Mathematics and Origami The succession of zeros and ones defines the folding sequence that was not so clear in Fujimoto ́s metho ...

Jesús de la Peña Hernández That is, values AE, AH, AK, AN ... tend to 7 1 , which is also the algebraic sum of terms like 2 (see ...

Mathematics and Origami In the case of producing 15 folds, we would have approached 7 1 up to the value of 0,1428527. 0,2856445 ...

Jesús de la Peña Hernández 10 REGULAR CONVEX POLYGONS WITH MORE THAN 4 SIDES Our attention will focus on folded constructions le ...

Mathematics and Origami 2 BDtgB CO= ; LH=HD=LB HD x senB= ()CO x x B − = 2 cos 2 tg LH CO x B − = x= 2 COcosB− 2 xcosB ; B CO B ...

Jesús de la Peña Hernández 6- Ang. CLM = Ang. CHG because of the symmetry with former step. Likewise, in pentagon CLMGH, Angs. i ...

Mathematics and Origami 10.1.4 PENTAGON WITH A PREVIOUS FOLDING Process shown in figs. A is common to pentagon, hexagon, heptago ...