MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández 1.3.2 INTERACTION OF STRAIGHT LINES AND SURFACES. We shall call paper strip to a rectangle such that ...

Mathematics and Origami 1.3.4 VERTICAL ANGLES 1.3.5 SUM OF THE ANGLES OF A TRIANGLE Let ́s produce the following folds in ∆ABC: ...

Jesús de la Peña Hernández HAGA ́s THEOREM Enunciation: Let the square FIJH whose side measures one unit. If we fold vertex F ...

Mathematics and Origami Under these conditions AB = AF; in other words, A is a point on the parabola p which has focus F, direct ...

Jesús de la Peña Hernández Let ́s pass to demonstrations. For x = 2 (^1) we have: 8 4 x= 8 5 y= 8 3 z= 6 4 a= 6 5 b= 6 3 c= 24 4 ...

Mathematics and Origami COROLLARY P Enunciation: Let ́s assume that in a square whose side measures one unit, any of its four ...

Jesús de la Peña Hernández OBTENTION OF PARALLELOGRAMS 6.1 SQUARE FROM A RECTANGLE Solution 1 Rectangle with sides in any give ...

Mathematics and Origami 6.5 RHOMBOID FROM A PAPER STRIP. Start up with the greater side AB and fold over small side AX with any ...

Jesús de la Peña Hernández 6.6 OBTENTION OF RECTANGLES WITH THEIR SIDES IN VARIOUS PROPORTIONS: 6.6.1 2:1, start up with a squar ...

Mathematics and Origami Let L and l be the greater and smaller side of the rectangle finally obtained in step 5. In 2 : CB = 2 L ...

Jesús de la Peña Hernández 6.6.6 (^2) :( 5 − 1 ) = ( 1 + 5 ): 2 x = tg α 2 2 1 = 1 : = ; AB BC AB x x x = = − ± − ± − 2 5 1 ...

Mathematics and Origami 6 So we get EH = EG + 1 = 2EF + 1 = 5. With successive folds similar to those of step 5, I and J are obt ...

Jesús de la Peña Hernández Let ́s recall what is the division of a segment in media and extreme ratio. When that division takes ...

Mathematics and Origami AC CB CB AB = ; CB^2 =AB×AC It is pertinent to quote now that rectangle ABCD in Point 6.6.6 is an auric ...

Jesús de la Peña Hernández 6.7 DYNAMIC RECTANGLES. SQUARE ROOT OF SUCCESSIVE NATURAL NUMBERS. PROCEDURE 1 (Fig. 1) Let ́s start ...

Mathematics and Origami 7- OV. Getting F; OF= 4 8- A → OF; O → O. Getting X 9- AO → AO; X → X. ,, : U 10- OU. Getting H; OH= 5 J ...

Jesús de la Peña Hernández 0 2 1 WY^2 + 2 WY− = ; WY= 1 2 3 − VY=WYcosα=WY×LY=WY() 1 −VY ; VY() 1 +WY =WY VY= 3 2 1 − Till no ...

Mathematics and Origami 3 Interlude 1 2 Fig. 1 brings out figs. 2 and 3 by me- rely changing the mountain / valley configuration ...

Jesús de la Peña Hernández 7 GEOMETRY IN THE PLANE. CARTESIAN PLANE. ALGEBRA. 7.1 AREA OF A RECTANGLE. That area is expressed by ...

Mathematics and Origami 7.2.2 SQUARES ́ DIFERENCE. Let squares A and B with respective sides x, y. Algebraically we know that: ( ...