The Otto Reichel's geometry of circles as an example of work with a gifted student in mathematics lessons in the second half of the 19th century

Abstract

The paper is devoted to the discussion of the tasks related to finding the geometric locus of points. These tasks were included in the article Beiträage fäar den Unterricht in der Geometrie (“Contribution to the
teaching of geometry”) by Otto Reichel (Thorn, 1866), a teacher of Torun gymnasium in the 1860s. The solution of most of these tasks went beyond the curricula determined by the then educational authorities. It is an example of self-extension of the mathematics curriculum by a teacher in a school for gifted students in order to better prepare young people for matriculation examinations, university studies, and later professional careers.