You cannot just assume that beauty is relative from the get-go.
Why not, if the idea of 'beauty' clearly varies from person to person, culture to culture, time period to time period, etc? That there is some absolute measure of 'beauty' is a claim that needs to be proven, because relative beauty that exists 'in the eye of the beholder' is quite apparent.
In western culture, for example, 150 years ago, women were seen to be more 'beautiful' if they were somewhat plump (well-fed but not fat) and pale in skin tone. Now, what is 'beautiful' for a woman in our culture is to be tanned and skinny. Of course there are a host of other things involved when determining if another person is 'beautiful' or attractive or not, including evolved psychological responses, facial expressions, tone of voice, social status etc...
It's also interesting that we talk of 'beauty' when referring to pleasurable sights and sounds, such as a painting or musical performance. But the other senses somehow do not convey 'beauty'...people typically do not say that a touch, smell, or taste is beautiful. What is it about sights and sounds that can be beautiful? Is beauty even something that can be logically determined, or do we just 'sense' beauty immediately when it hits us...because in my experience, it is the latter.