Disclosing: Lambert's case and Pi's irrationality

Abstract

This text presents an attempt to ensure that a public possibly without specialized scientific training has a fairly accurate idea of the proof of the irrational character of the number ?. The proof of this property was obtained in the eighteenth century by the sage Johann Heinrich Lambert, also known for many other inventions and contributions, such as the introduction in mathematics of hyperbolic functions or the definition and use of projections in cartography. The complete demonstration of the irrationality of ? is of a bachelor's degree in mathematics, but we believe that the presentation of the mathematical tools used by Lambert for his test is not only for specialists, but also beneficial for all audiences. The use of technology can introduce into the presentation a sensitive approach for that purpose. Conditions for the feasibility of a scientific dissemination text accessible to all public are stated.