The beautifully smooth egg shown below is composed of circular segments that fit together ‘continuously’, so that there is no sudden change in the ‘direction’ of the shell, where any two segments touch.
The Problem :
Reconstruct the egg yourself, using only a compass and a ‘straight edge’ ( even for the initial triangle ! )
What aspect of the construction ensures that the egg is smooth at the junction of any two dissimilar segments ?
Change the shape of the initial triangle, and see what difference this makes to the shape of the egg. Which shape of triangle makes for the most ‘natural-looking’ egg ?
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