It is deep experience of meanings in geometry (and indeed in all of mathematics and well as art and engineering) that we believe deserve to be called aesthetic experiences. We believe that mathematics is a natural and deep part of human experience and that experiences of meaning in mathematics should be accessible to everyone. Much of mathematics is not accessible through formal approaches except to those with specialized learning. However, through the use of non-formal experience and geometric imagery, many levels of meaning in mathematics can be opened up in a way that most people can experience and find intellectually challenging and stimulating. Many formal aspects of mathematics have now been mechanized and this mechanization is widely available on personal computers or even handheld calculators, but the experience of meaning in mathematics is still a human enterprise. Experiencing meanings is vital for anyone who wishes to understand mathematics, or anyone wishing to understand something in their experience through the vehicle of mathematics. We observe in ourselves and in our students that these are, at their core, aesthetic experiences. In this paper we will tell some stories of our experience of meanings in geometry and art. David's story starts with art and ends with geometry, while Daina's story starts with geometry and ends with art. However we both share the bulk in the middle, including experiences of non-Euclidean geometries and kinematics models.