MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández 7.15 PROGRESSIONS 7.15.1 ARITHMETIC PROGRESSIONS They are formed by a succession of quantities such t ...

Mathematics and Origami 2 = i−^1 + i+^1 i a a a ; 3 2 4 1 1 1 1 2 3 2 2 4 2 3 2 a d a a a a d a d a d a = + = + = + + + = + = Re ...

Jesús de la Peña Hernández so, it will be 9. 2 1. 111 1 2. 2458 1. 111 1. 4742 = − × − S= on the other hand, if we add up the 5 ...

Mathematics and Origami We may observe that odd segments succession is a geometric progression with ratio 1 / 2. Same happens wi ...

Jesús de la Peña Hernández 8 SQUARES / TRIANGLES / VARIOUS 8.1 SQUARE WITH HALF THE AREA OF ANOTHER ONE. 8.1.1 FOLDING SOLUTIONS ...

Mathematics and Origami Solution 2 (very simple) 8.2 OBTENTION OF TRIANGLES 8.2.1 ISOSCELES RIGHT ANGLED TRIANGLES FROM A SQUARE ...

Jesús de la Peña Hernández A version of the latter case consists in cutting the triangle out of the square: 8.2.2.2 MAXIMUM EQUI ...

Mathematics and Origami Solution 2 Solution 3 CD = 1 ; ∆ACD, equilateral ; ang. ACD = 60º ; ang. ECD = 30º DE=tg 30 ; tg 30 1 = ...

Jesús de la Peña Hernández If we take O as the mid-point of MN, we ́ll have: () = =       = + +       OA= AM+AN ...

Mathematics and Origami 8.2.3 EQUILATERAL TRIANGLE FROM A RECTANGLE (three solutions) Solution 1 The rectangle is a paper strip, ...

Jesús de la Peña Hernández implies the following proportion between a (height) and b (base):a b 4 3 ≥. If a b 4 3 > , an equi ...

Mathematics and Origami 8.2.5 STELLATE TRIANGLE Now is the occasion to recall point 6.9 (stellate rectangle) in which the triang ...

Jesús de la Peña Hernández 8.2.7 ANOTHER CURIOSITY Right-angled triangle ABC is the result of the two successive folds. To prove ...

Mathematics and Origami 8.2.8 SINGULAR POINTS IN TRIANGLES 8.2.8.1 ORTHOCENTER It ́s the intersection point of the three altitud ...

Jesús de la Peña Hernández That is, O is equidistant from A, B, C; in consequence O is the center of the unique circumfer- ence ...

Mathematics and Origami 8.2.8.4 INCENTER Is the intersection of the three bisectors of a triangle. 1- Fold the three bisectors t ...

Jesús de la Peña Hernández The square at left (white obverse and obscure reverse) was rumpled fortuitously in the hand; before t ...

Mathematics and Origami To fold flat around O, we have these possibilities: Fig. 1 is an enlargement of central node O in the sq ...

Jesús de la Peña Hernández JARITA”, the bulletín of the AEP entitled Introduction to creation). On the contrary, we are going to ...

Mathematics and Origami This way we have got points on the hyperbola such as C 1 C 2 C3, besides C and V. The design of a foldin ...