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| All my stained glass work is based on numbers. They come in any form from just counting the pieces of glass
in an object to calculated surfaces, be it in 2D or 3D. I only use flat glass, even for curves and spirals. And I can cut the vast majority of the pieces along a straight edge. Yes, it is math I am talking about! The following lines are a short explanation of the shapes I work with and a bit of theory around them. There is no harm in skipping all this, just as it may kindle your interest if you continue. Two dimensional geometry as layed out by Euclid is mostly unchanged to this day. New geometries have been found and developed though, like tesselations (tilings), projective geometry and so on.Solid geometry deals with space enclosed by surfaces, or faces. So we can say that the space of a cube is enclosed by six squares (hence the proper name hexahedron. Hexa is Greek for six, hedron means face). A square is a regular polygon (poly = many, gon = side) with four sides, that is all sides are the same, and all angles are the same. A regular polyhedron would therefore be made up of regular polygons. Only four more regular polyhedra are possible: the tetrahedron, made up of four (tetra = four) equilateral triangles, the octahedron (octa = eight) made up of eight equilateral triangles, the icosahedron (icosa = twenty) with twenty equilateral triangles and lastly the dodecahedron, comprised of twelve pentagons (do = two, deca = ten, 2+10=12). But that is not all. These five regular solids, the Platonic Solids, have relationships to one another. If all midpoints of the faces of a solid are connected to the face next to it we get another regular solid. In the case of the tetrahedron there will be another tetrahedron inside, albeit upside down from the original. When the midpoints of the faces of a hexahedron (cube) are connected to the faces next to it we find an octahedron, and, upon connecting the midpoints of the faces of an dodecahedron to the faces next to it we have an icosahedron. And this works both ways: an icosahedron has a dodecahedron in it, the cube is dual to the octahedron and the tetrahedron is, you guessed it, self-dual. With the introduction of different rules for solid shapes Archimedes, Kepler and a long line of others have found new shapes.And the dicussion about the sphere being the sixth Platonic Solid with an infinite number of surface points still goes on! |
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The Family Resource Center is offering my workshop. Take a look!
| Glass Geometry Hans Schepker 325 Breed Road Harrisville, NH 03450 w 603.827.3014 c 603.721.2216 f 603.827.3115 |
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-All artwork, images and designs in this site are (C) Hans Schepker 2003-07 -All tyepoos, oppinionses and blunderers are also mine 8( |
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