Everyone is familiar with distributivity of multiplication over addition of real numbers. The distributivity of two binary operations sometimes goes both ways (e.g. max and min, or for lattices in general.)
Out of curiosity, I looked at the set of real numbers for which addition distributes over multiplication. A simple computation shows that this set is
$$\{a,b,c\in \mathbb{R}\, |\, a+b+c=1\}.$$
Is this just a meaningless fluke, or is there reason to expect something like this?