Figures in Motion: Geometric Transformations in Secondary School Mathematics, 1874–1906

The paper is an examination of geometric transformations in the plane as they appeared in texts by Charles Méray (1874), Émile Borel (1910), and Jacques Hadamard (1906)—all from France—and Julius Henrici and Peter Treutlein (1881) from Germany. The transformations are the dilation (homothétie), translation, reflection, and rotation; the paper includes a brief introduction to the transformations themselves. The effect on the secondary school curriculum was especially pronounced in France. Interest in transformations waned in the years of the two world wars, only to reappear, in slightly different form in the 1970s with the “New Math” movement in the United States. The flowering at the end of the nineteenth century grew from decades-long developments in education reform, mathematical analysis of the movement of invariant bodies, and the Erlanger Program.