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Research
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synclastic raising |
synclastic sinking |
anticlastic forming |
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The main aim of this research has been to arrive at a proper understanding and documentation of the transformation of shape taking place in the deformation of flat templates into three-dimensional forms. A lot can be done with the basic anticlastic 'channel' (below left, generally formed to a stronger degree). Michael Good has developed a great variety of forms based on this process. One interesting transformation is the helicoid, which can be created by 'shifting the orientation of curvature'. In the channel the principal curvatures follow the longitudinal 'axis' of the strip and the perpendicular curved cross-section. In the helicoid the curvatures are oriented at 45 degrees to the long, straight axis and its straight cross-section.The Irish silversmith/metalsmith Brian Clarke
Michael Good have also undertaken some research on the creation of
ancient Celtic anticlastic torques, which show a high level of
technical expertise. So in this respect anticlastic forming techniques
have been around for a long time.
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forming a 'channel' |
shifting the orientation |
channel and helicoid |
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The forms I wanted to create varied in their ratio, orientation and degree of curvature in different sections of the forms and occasionally included synclastic (domed) sections This required a careful planning of both the forming process and the templates. A basic case is the Möbius band which can be simplified as a rectangular strip going through a 180 degree twist while closing back in on itself to form a circle. This not only involves a change of orientation but also of the location of the centre of the saddle in different sections of the form. |
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twofold möbius strip |
threefold möbius strip |
minimal möbius |
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The geometrical implications of these
transformations pointed towards the mathematical investigation of
minimal (area) surfaces, which is a branch of topology. Such surfaces
can be observed by dipping a non-planar wire frame into a soap
solution, which naturally seeks to minimise tension and thus, its
surface area. The connection to minimal surfaces is also apparent in
the work of several American sculptors, Brent Collins, Robert Longhurst and Charles O. Perry, Bathsheba
Grossman, and some sculptors/mathematicians make use
of the principle in more explicit ways (Stewart
Dickson, Carlo
Sequin and Helaman Ferguson).
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Form and Mathematics
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copyright©Benjamin Storch2007 |