Beauty is the extensive ability of unexpected applications, estimated usually in the visual way.
Beautiful product, often a text of an image, carries more information, than it could be expected. Beautiful tool allows the extensive range of abilities without affecting its efficiency in the main purpose. Beautiful formula allows wide range of applications.
Beauty is often usually estimated visually, as an impression of hopes for the extremal efficiency and universality. Therefore, criteria of beauty are subjective and cause discussions. The beauty contests lead to unification of criteria of beauty; then these criteria can be expressed in some physical and mathematical way. (Especially such a criteria may apply to the beauty of a human body.)
The activity on creation of beautiful objects is called art. Often the products of art are attractive, causing an impression that the spectators also can make beautiful things; in many cases, in some degree, it is really so. Such an extension of the abilities of the consumers of art is the application and the justification.
Beautiful things bring not only the ability of the direct application but also knowledge, how to create things in the efficient way. In the so-called "pure art" such a knowledge dominate; in this sense the products of art may be "just beautiful".
http://www.youtube.com/watch?v=MqzNojwSPzE Pollardrho06. Hidden in the Euler’s Identity is the ‘Story of CREATION’ and this is what makes it most beautiful. Sep 27, 2008