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my stained glass work isbased on numbers. They come in any form from
just counting the piecesof glassin an object to calculated surfaces, be
it in 2D, 3D or 4D in 3-Space. 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 withand 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 laid 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 discussion about the sphere being the sixth Platonic Solid with an infinite number of surface points still goes on! |
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| Some items can be purchased at my EBay store |
!! Immersion In The Arts
Camp 2012 Info and Application
online NOW !!
(.doc file here)
| New mixed age and adult weekend workshops |
This link gets you to my calendar.
| Glass Geometry Hans Schepker 325 Breed Road Harrisville, NH 03450 cell-603.721.2222 |
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-All artwork, images and designs in this site are (C) Hans Schepker 2003-08 -All tiepoos, oppinionses and blunderers are also mine 8( |
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Based on a style sheet of JAlbum 7.2& Chameleon