The mathematics curriculum in the secondary school normally includes a single one-year course in plane geometry or, perhaps, a course in geometry and elementary analytic geometry called tenth-year mathematics. This course, presented early in the student's secondary school career, is usually his sole exposure to the subject. In contrast, the mathematically minded student has the opportunity of studying elementary algebra, intermediate algebra, and even advanced algebra. It is natural, therefore, to expect a bias in favor of algebra and against geometry. Moreover, misguided enthusiasts lead the student to believe that geometry is “outside the main stream of mathematics” and that analysis or set theory should supersede it.

Perhaps the inferior status of geometry in the school curriculum stems from a lack of familiarity on the part of educators with the nature of geometry and with advances that have taken place in its development. These advances include many beautiful results such as Brianchon's Theorem (Section 3.9), Feuerbach's Theorem (Section 5.6), the Petersen–Schoute Theorem (Section 4.8) and Morley's Theorem (Section 2.9). Historically, it must be remembered that Euclid wrote for mature persons preparing for the study of philosophy. Until our own century, one of the chief reasons for teaching geometry was that its axiomatic method was considered the best introduction to deductive reasoning. Naturally, the formal method was stressed for effective educational purposes.