Origami Heaven

A paperfolding paradise

The website of writer and paperfolding designer David Mitchell

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La Ensenanza del Trabajo Manuel by Pedro de Alcántara García and Teodosio Leal y Quiroga, 1903
 
'La Ensenanza del Trabajo Manuel' by Pedro de Alcántara García and Teodosio Leal y Quiroga was published in Madrid in 1903.

A full copy can be accessed online at http://bdh-rd.bne.es/viewer.vm?id=0000076174&page=1 Anyone interested in the history of teaching mathematics through paperfolding should refer to the full text which is an important source on this subject and contains much information not referred to here.

The book makes use of paperfolding at three different levels:

In Grado Primero

The first part of this section consists of a series of simple folding exercises which produce some simple Folds of Beauty, notably a square showing an internal four-pointed star, and several well-known Folds of Life, the Table with four legs, the Windmill and the Double Boat. There is also a description of the Cut and Fold Windmill but no drawing to accompany this.

The Internal Four-Pointed Star

The Table (pictured upside down)

The Windmill

The Double Boat

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La Flecha (The Arrow) - Wooden Dart with Paper Flights

This section describes how to fold a waterbomb base and then how to attach it as a flight to a wooden dowel, which is either, in the case of young children, sharpened to a point, or in the case of older children, fitted with a pen nib to act as a point.

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The Windmill Base

This section explains how to fold a windmill base and how to develop it to produce further basic patterns.

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Paper Filter

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Six-Pointed Star from an Equilateral Triangle

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Designs folded from Pentagons

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Designs folded from Hexagons

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The next section, entitled 'Recortado' shows how to derive various shapes by folding and cutting paper and how to cut a sheet of paper folded just once into shapes which possess reflective symmetry.

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In Grado Segundo

The first part of this section of the book shows how to fold a square into various kinds of grids and how to use these grids mathematically. It also includes exercises on working out the area of folded shapes in relation to a square drawn around them. These shapes include the Windmill from Grado Primero and the Pajarita. No folding instructions for the Pajarita are given.

The Pajarita

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The Rectangular Packet

This is described as 'the bag so useful in pharmacies'.

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Bonnete de Magico - The Magic Hat

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Packet for Seeds - The Hexagonal Packet

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Metamorphosis of the Frog - The Blow-up Frog

No instructions for folding this design, other than the pictures below, are given.

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The Froebel Star

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Cross made of Froebel Stars

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Strip Folding Designs

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There is also a 'Recortado' chapter in this section which shows how to use paperfolding to create designs with double, triple, pentagonal and hexagonal symmetry.

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The Sphere

This design is similar to the XYZ Ball except that it has more pieces and some of the pieces are folded in half.

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Cut and Fold Polyhedral Nets

This section gives nets, or in some cases partial nets, for creating the tetrahedron, the stellated tetrahedron, the cube, the octahedron, the compound of five tetrahedra, the dodecahedron, the icosahedron then shows how to create compound forms which correspond to chemical molecules by adding cubes and octahedra together.

Finally the author gives a net for a polyhedra which will wrap the combination of seven cubes.

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In Grado Tercero

Cut and Fold Polyhedral Nets

This section gives partial nets to construct three more compound polyhedra.

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