I read this article and decided to try composing and decomposing unit fractions for myself. Several notepads some coffee and a ballpoint pen later I have created a neat method of splitting 1 into a maximum number of different unit fractions below one hundredth.
My method stretches the rules above, by using numerators and denominators higher than 1/99 during construction. But it is simple, elegant and can be quickly calculated on a sheet of paper. I am confident that I could produce a proof of the maximum number of unit fractions (below one hundredth) that decompose 1. Is this something new or am I rediscovering the wheel, or just missing something? I would love to share my idea with somebody in the know. Thanks again for the inspiring article!