The figure below shows two squares ABCD and EFGH so that A, D, E,
and H are collinear points. Line AF cuts BE at J and BH at K, Line DF cuts
BE at L and BH at M. If area AJLD = S_{1}, area BKJ = S_{2},
area KFM = S_{3}, and
area LMHE = S_{4}, prove that S_{1} + S_{3} = S_{2} + S_{4}.

### Geometric Art of Problem 1426: Sketching, Typography, iPad Apps

### Animation of the Conformal Mapping or Transformation of Problem 1426

### Conformal Mapping

A conformal mapping or conformal transformation is a continuous mapping preserving the form of infinitesimal figures. This conformal map produces a realistic view of the original image or map.
This the conformal transformation of
problem1426

See also:
Typography and poster of problem 1417.