The Appolonius circle is a theorem in pure geometry. It is used in the 'method of images' in physics. And not just for ancient textbook problems either. I saw a paper in experimental fluid mechanics that builds up the intuition with images (2D incompressible flow). Appolonius live and kicking in the 21st century.
The Kochen-Specker theorem is interesting (if not useful). The proofs have a similar flavour to Sylvester. One tries to make a set of projections 'compatible' and it turns out to be impossible. Maybe there's a deeper connection.
The Kochen-Specker theorem is interesting (if not useful). The proofs have a similar flavour to Sylvester. One tries to make a set of projections 'compatible' and it turns out to be impossible. Maybe there's a deeper connection.