Descriptive Geometry, The Spread of a Polytechnic Art

Evelyne Barbin was previously a professor of epistemology and history of sciences at the University of Nantes (France). Since 2014, she is now professor emeritus at the University of Nantes. She is a member of the Laboratory of Mathematics Jean Leray CNRS UMR 6629, where she is in charge of the research group on history of mathematics. She taught history of mathematics and sciences in all levels of teaching from licence to master. She was the director of 15 theses on the history of mathematics and sciences. Her research concerns three fields: history of mathematics, history of mathematics teachings, and relations between history and teaching of mathematics. The main themes of her historical research are: mathematical proofs in history, mathematics and sciences in the 17th and 19th centuries, and history of mathematics teaching from the 19th to the 20th century. She has worked at the IREM (Institute for Research on Mathematics Education) since 1975. As convenor of the National Committee of the IREM "Epistemology and History of Mathematics", she has organized 20 national colloquia, 8 interdisciplinary Summer Universities on history and teaching mathematics, and the first European Summer University (ESU) "Epistemology and History in Mathematics Education" in 1993. She was chair of seven ESUs from 1996 to 2014. Since 1980, she has also been a member of the International Study Group on the Relations between History and Pedagogy of Mathematics (HPM). She was the chair of HPM from 2008 to 2012. Marta Menghini is an associate professor in the Department of Mathematics of the University of Rome Sapienza. She is the author of numerous published works in the fields of Mathematics Education, History of Mathematics, and the History of Mathematics Education. She was in the Scientific Committee and chaired the Organizing Committee of the International Symposium held in Rome in March 2008, "The First Century of the International Commission on Mathematical Instruction: Reflecting and Shaping the World of Mathematics Education", and edited the volume published on this occasion by Enciclopedia Italiana. In 2012, she held a Regular Lecture at ICME 12 in Seoul. She wrote, with Evelyne Barbin, the Chapter on "History of Teaching Geometry" in the International Handbook on the History of Mathematics Education. She was involved in the translation of Felix Klein's third volume on "Elementary Mathematics from a Higher Standpoint", which appeared in 2016. Klaus Volkert is a full professor at the University of Wuppertal; he lectures on mathematics, didactics, and history. His interests are mainly in the history of geometry and topology, and recently he started a project on Wilhelm Fiedler. He is Editor in Chief of the journal "Mathematische Semesterberichte" (together with J. Steuding) and editor of the series "Mathematik im Kontext" (with David Rowe).

Part I: First Spreading in Western Europe.- Chapter 1: Monge's Descriptive Geometry: his Lessons and the Teachings given by Lacroix and Hachette.- Chapter 2: Descriptive Geometry in France: Circulation, Transformation, Recognition (1795-1905).- Chapter 3: Descriptive Geometry in Italy in the 19th Century: Spread, Popularization, Teaching.- Chapter 4: Luigi Cremona and Wilhelm Fiedler: the Link between Descriptive and Projective Geometry in Technical Instruction.- Chapter 5: Descriptive Geometry in 19th Century Spain: from Monge to Cirodde.- Chapter 6: Descriptive Geometry in Spain and the Emergence of the late Modern European outlook on the Relationship between Pure Science and Technology.- Chapter 7: Portuguese books of Descriptive Geometry, from University and Polytechnic to Secondary School.- Part II: Installation of Descriptive Geometry in Europe.- Chapter 8: A German Interpreting of Descriptive Geometry and Polytechnic.- Chapter 9: The Evolution of Descriptive Geometry in Austria.- Chapter 10: The Vienna School of Descriptive Geometry.- Chapter 11: Otto Wilhelm Fiedler and the Synthesis of Projective and Descriptive Geometry.- Chapter 12: At the Crossroads of two Engineering Cultures, or An Unedited Story of the French Polytechnician Charles Potier's Descriptive Geometry Books in Russia.- Chapter 13: Engineering Studies and Secondary Education: Descriptive Geometry in the Netherlands (1820-1960).- Chapter 14: In Pursuit of Monge's Ideal: the Introduction of Descriptive Geometry in the Educational Institutions in Greece during the 19th Century.- Chapter 15: The Rise and Fall of Descriptive Geometry in Denmark.- Chapter 16: Descriptive Geometry at Czech Technical Universities until 1939.- Chapter 17: The Love Affair with Descriptive Geometry: Its History in Serbia.- Chapter 18: Descriptive Geometry in England - Lost in Translation.- Part III: Descriptive Geometry in America and Africa.- Chapter 19: Teaching of Descriptive Geometry in the United States (1817-1915): Circulation among Military Engineers, Scholars and Draftsmen.- Chapter 20: The Teaching of Descriptive Geometry in Egypt (1837-1902).- Chapter 21: The Dissemination of Descriptive Geometry in Latin America.- Part IV: Epilogue.- Chapter 22: The Myth of the Polytechnic School.

"I learned much from this book and it caused me to reflect on various aspects of mathematics education in ways I would have not have before. ... I warmly recommend mathematics educators to include Évelyne Barbin, Marta Menghini, and Klaus Volkert's volume on their bookshelves." (Michael N. Fried,Educational Studies in Mathematics, Vol. 106, 2021)