My main research interest for most of my working life has been solving problems with lattice points. An intial interest in elementary geometry problems in the plane became a fascination after hearing a talk by Professor Paul Erdös in 1972.
“The secret to research,” he said, “is to ask questions. Some of the questions you ask will be silly. Others will turn out to be trivial. But every now and then you will ask a question that will lead to a good problem.”
So began my research career, with the discovery that the geometrical problems I enjoyed playing with could be counted as research and lead to published papers.
These lattice point problems have great appeal to me because they are easy to understand, and do not require a great deal of mathematical background. Of course finding the solution may be a different matter! They are therefore problems which can be easily explored, and I have found just as much joy in discovering new problems as in solving old ones.
The purpose of this site is to present some of these problems in a discovery context – to share some of the great pleasure and satisfaction that this area of mathematics has given me. References are given for most of the solutions, especially for those which are more difficult. More difficult problems have been omitted, but I would be very pleased to receive suggestions concerning the inclusion of material which does not appear here, but which readers consider might be easily accessible to the amateur.
