This paper is concerned with the interactions between medics and biologists on the one hand, the 'anatomists' of the title, and 'geometers', or engineers and physicists, on the other. It was delivered as the 16th annual Samuel Haughton Lecture on 23rd January 2010 at the Bioengineering in Ireland conference in Malahide. The paper begins with Samuel Haughton, the father of Irish biomechanics, and then discusses how anatomists and geometers have cooperated to solve problems in the areas of bone adaptation, fatigue microdamage, osteoporosis, third-level education and even art.