How to check 3D congruence by comparing the shape of "elements-lines"Regard a straight line from somewhere near the center of the shell to the outline to mark out the place of an "element".
The isoline drawings on the following pages have been completed with a number of such "elements". Equal numbers show where equal "elements" where found on both "upper" and "lower" parts of the arch.
To find out where equal "elements" are positioned one has to start marking out the place for one of them by drawing a straight line (marking out the place of the cross section to be checked). The location of an other one has to be searched for. The cross sectional shape of elements are equal when the distances between a number of intersection points with the isolines following on each other coincid with those already marked on the paper. Each isoline represent a very special height on the surface of the shell. The arcshape of an "element" that can be constructed is determined by the location of the intersection points of "the element line" with the "isolines".
This congruence can be checked in the following way:
1. Hold a piece of paper close to a drawn "element line" and mark the points of intersecting isolines on the edge of the paper.
2. Move the edge of the piece of paper around the isoline drawing in order to find the place where these marks coincid (intersect) with the isolines. When this happens an equal "element" has been found.
It is possible to find an almost countless number of such congruent pair of "element-lines" based upon the 3D geometry described on the previous pages.
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