Folding a triangle

Extract

The Original problem

Take a right-angled triangle ABC, where ∠C = 90°, and fold along UV so that C lies on AB, as shown in Figure 1, where C' is the new position of C.

Problem: Where should one fold in order to minimise the area of the folded triangld CUV?

This problem was discussed by Hirschhom in [1], where he gives its origins and provides a solution, describing the answer as ‘quite remarkable’. However, he does not relate the answer to the geometry of the configuration. We adopt a more geometrical approach and use some simple folding ideas—there is a close relationship between paper folding and geometry which deserves to be more widely known (see [2] for example).