A fair curve is something that even the untrained eye can appreciate. It may be taken for granted when it is fair and true but it is easy to see when it is not fair and true. It will stick out like a sore thumb.
A fair curve does not need to be constant like a section of a perfect circle. It can have a changing radius along its length. I love this curve of my Waltham arm chair rail where it transitions from the side to the back of the chair. Complex , yet simple. Or simple but complex.
See all of my chairs here.