Angles in Secondary School: Surveying and Navigation -- Dividing a Triangle in the Middle Ages: An Example From the Latin Works on Practical Geometry -- A Square in a Triangle -- Indian Calculation: The Rule of Three--Quite a Story -- The Arithmetic of Juan de Ortega: Equations without Algebra -- The Congruence Machine of the Carissan Brothers -- A Graphical Approach to Euler’s Method -- Calculating with Hyperbolas and Parabolas -- When Leibniz Plays Dice -- The Probability of Causes According to Condorcet.

This book brings together 10 experiments which introduce historical perspectives into mathematics classrooms for 11 to 18-year-olds. The authors suggest that students should not only read ancient texts, but also should construct, draw and manipulate. The different chapters refer to ancient Greek, Indian, Chinese and Arabic mathematics as well as to contemporary mathematics. Students are introduced to well-known mathematicians—such as Gottfried Leibniz and Leonard Euler—as well as to less famous practitioners and engineers. Always, there is the attempt to associate the experiments with their scientific and cultural contexts. One of the main values of history is to show that the notions and concepts we teach were invented to solve problems. The different chapters of this collection all have, as their starting points, historic problems—mathematical or not. These are problems of exchanging and sharing, of dividing figures and volumes as well as engineers’ problems, calculations, equations and congruence. The mathematical reasoning which accompanies these actions is illustrated by the use of drawings, folding, graphical constructions and the production of machines.