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Caption: Mathematical Models Catalog of a Collection of Models of Ruled Surfaces
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33 If the curve A B O D E degenerates into a single point, there will occur some singularities which will mask the general properties of these surfaces. This degeneration gives conical surfaces. W h e n , further, the single point in question moves off to infinity, w e get the cylindrical surfaces. This is not all. If w e take two cards, counterparts of one another, and glue them together along the polygon A B O D E , w e can deform the double plane into a double polyhedron, the twro sheets of which will be placed back to back. There will then be a finite angle between the corresponding gores in the two sheets. W h e n w e replace this polygon by a curve, this angle will be infinitesimal, and a section at right angles to A B C D E will be a cusped curve, Each sheet will evidently be a ruled surface, the variable right lines of which will touch the curve which replaces the polygon A B O D E . It is evident that the right line generators must otherwise stop abruptly, for they could not get from one sheet to the other on any different conditions. A good imitation of this can be made by taking two sheets of paper,fittedover one another, as A B 0 D , cutting out a curved piece ( E F Gr) from both, and laying a smear of strong glue along E F G , so as to fasten them together L*1 2991)2,
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