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Mathematics today isn't just one subject, it's dozens of subjects. In the last hundred years, and particularly in the last fifty, our knowledge has increased at an unprecedented rate, and it is only right that our school curriculum has evolved in the light of the new discoveries. It is with some regret, however, that we have had to let go of many beautiful old problems of synthetic geometry.
About 1875, Euclidean geometry experienced a meteoric revival that saw hundreds of marvelous new results published in the next half century. Two outstanding books in this field are Nathan Altschiller Court's College Geometry and Roger Johnson's Advanced Euclidean Geometry; also, anyone attracted to geometry will be sure to enjoy Coxeter and Greitzer's Geometry Revisited.
Synthetic geometry is obviously a chain subject, and although many of the new results are of an elementary nature, they often concern fairly complicated configurations and can only be approached comfortably after substantial preliminary discussion; assuredly any effort directed toward their appreciation is always well rewarded. Fortunately, a good number of these delightful little gems can be enjoyed by recalling just a few well-known theorems and deriving an occasional preliminary result.
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