Some Models for Teaching of Geometry and Mechanics

EasyChair Preprint no. 7980

Abstract

The modern education and teaching of higher geometry and mechanics is not possible without physical and digital models. There are many examples in the history of mathematics that models were seen as a necessary element of learning. At the end of the 19th century, in his lectures, the famous German mathematician Felix Klein insisted on the importance of creating the models for the development of intuition in students and as a tool to combat the excessive abstractness of mathematics. The book "Visual Geometry" (Anschauliche Geometrie) by D. Hilbert and S. Cohn-Vossen, published in German in 1932 in Berlin, contains photographs of many models as illustrations. These models produced in workshops by Martin Schilling in Germany. There is a catalog for mathematical models of this workshop (Catalog mathematischer modelle for den hooheren mathematischen Unterricht. Leipzig: Verlag von Martin Schilling, 1911). Many Universities in the world purchased these models. Some models from this catalog are present in the collection of Saint- Petersburg State University in Russia. We will deal with a model for "rolling of a hyperboloid on a hyperboloid". 

 At Saint-Petersburg State University (the theoretical mechanics direction) among the modern courses for two-year students there is an individual coursework (a term paper). This year, one of the students (Aleksandr Cherenkov) chose a term paper on creating a computer model in mechanics from the website www.etudes.ru. The model had to be created by a computer means in the form ready for printing on a 3D printer. His report "Model in mechanics "rotation of the generatrix of the hyperboloid" (under the supervision by docent G. Kuteeva and engineer K. Tverev) was listened to with attention and received approval. The next step in this work is to make a computer model for an illustration from the book "Visual Geometry" by D. Hilbert and S. Cohn-Vossen, a model for "rolling of a hyperboloid on a hyperboloid".

Keyphrases: kinematic models, rolling of a hyperboloid on a hyperboloid, rotation of the generatrix of the hyperboloid, Visual geometry, workshops by Martin Schilling

@Booklet{EasyChair:7980,
  author = {Galina Kuteeva and Konstantin Tverev and Aleksandr Cherenkov},
  title = {Some Models for Teaching of Geometry and Mechanics},
  howpublished = {EasyChair Preprint no. 7980},

  year = {EasyChair, 2022}}