Mrs. Miniver’s Problem

mrs. miniver's problem

One of Jan Struther’s popular stories of the 1930s included the following passage:

She saw every relationship as a pair of intersecting circles. It would seem at first glance that the more they overlapped the better the relationship; but this is not so. Beyond a certain point the law of diminishing returns sets in, and there are not enough private resources left on either side to enrich the life that is shared. Probably perfection is reached when the area of the two outer crescents, added together, is exactly equal to that of the leaf-shaped piece in the middle. On paper there must be some neat mathematical formula for arriving at this; in life, none.

Interestingly, mathematicians who pursued the problem found that no precise solution is possible. With circles, as with relationships, we have to do the best we can.