It seems that, ever since first meeting the ham sandwich theorem fourteen years ago, I have had a lurking interest in halving shapes. Somehow a few months ago I turned my attention more specifically to the problem of halving triangles and tetrahedra—a problem with which I am still wrestling. This problem was going to be the subject of an article for the Gazette, but it did not really work out well. In a letter about this abortive article Douglas Quadling drew my attention to the significance of hyperbolae for halving triangles—something which I had previously not noticed.