MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández Thus, mountain and valley folds in Fig. 3 are what we need to get a flat-folded figure. We may observ ...

Mathematics and Origami 8.3 VARIOUS 8.3.1 HOMOTOMIC FIGURES Din A Pseudo Din A right-angled isosceles ∆ If we divide successivel ...

Jesús de la Peña Hernández 2 Escalen right triangle Tangramlike demonstration of Fig.1 is correct when b c 3 4 = (a c 3 5 = ). I ...

Mathematics and Origami 3 Any scalene right triangle ABC From ∆abc we ́ll construct the exterior square with side CK = a+b. Then ...

Jesús de la Peña Hernández 8.3.4 PYTHAGOREAN UNITS Demonstrations made in point 8.3.3 for the Pythagorean theorem are adequate f ...

Mathematics and Origami Piece B (two units) Piece C (four units) Piece D (five units) (^4) A 567 (^56) 7 10 9 8 4 A 9 C (^101112 ...

Jesús de la Peña Hernández Piece E (five units) Therefore, the five pieces obtained are: The square A6; the isosceles right tria ...

Mathematics and Origami Remarks: Piece C10 is not the triangle ABC in Fig. 1. In this, BC ≠ AD (being AD= 1). There is a small ...

Jesús de la Peña Hernández 8.3.5 UNIT SQUARES (JEAN JOHNSON) Begin with a square folded as indicated in figs. 1 to 6. An irregul ...

Mathematics and Origami 9 DIVISION IN EQUAL PARTS 9.1 EVEN PARTS OF A PERIGON Begin with an irregular piece of paper to divide t ...

Jesús de la Peña Hernández 9.4 A SQUARE IN THREE EQUAL PARTS (five exact solutions) Solution 1 Solution 2 Solution 3 Square with ...

Mathematics and Origami Solution 4 Solution 5 9.5 A SQUARE IN THREE EQUAL PARTS (two approximate solutions) Solution 1 Side BC o ...

Jesús de la Peña Hernández Using D as a reference, mountain and valley fold (not flattening), to obtain a bellows con- figurati ...

Mathematics and Origami HI=EF ; 16 1 32 2 2 GH= 2 HI= = In ∆HAJ: ang H = 45º ; ang A = 22. 5 º 2 45 = ; ang J = 180 – 45 – 22.5 ...

Jesús de la Peña Hernández 9.7 A SQUARE IN THREE EQUAL PARTS (Corollary P) This is a consequence of the fact that a / x is biuni ...

Mathematics and Origami 9.9 TRISECTION OF ANY ANGLE ABC ∆BKL = ∆KLF (symmetry) ; BL = LF (symmetry) ∆BLD = ∆KLF (one side and an ...

Jesús de la Peña Hernández 9.10 TRISECTION OF ANY ANGLE (H. HUZITA) Let AIB = 3α the angle to trisect. In Point 7.14.5 this equa ...

Mathematics and Origami And the forth vector: [(4,3a) → (4,4a)] (which gives the axle 2a,X) a D I C 1 2 3 4 5 A 4a 2a 3a B Y F ...

Jesús de la Peña Hernández 9.11 A SQUARE IN FIVE EQUAL PARTS Let ́s begin with a square of one unit side: α α senα 2 1 x=PBsen = ...

Mathematics and Origami Now then, there are publications which affirm that 7 3 GD= without any clarification whether that is e ...