An analysis of two 19th century Norwegian geometry books, and the reactions they caused
Bernt Michael Holmboe (1795–1850), professor in mathematics, wrote several textbooks on mathematics, and his presentation of geometry was traditional and in conformity with Euclidean ideas. Christopher Hansteen (1784–1873), professor in applied mathematics, wrote a textbook on geometry where he challenged the traditional Euclidean geometry. This paper analyses two very different approaches to basic definitions in the two geometry textbooks written by Holmboe and Hansteen, and what reactions this caused in the contemporary society. The main focus will be on the understanding of basic concepts in geometry, and of parallel lines and Euclid’s parallel postulate.
Andreas Christiansen is associate professor at the Department of teacher education and cultural studies at Stord/Haugesund university college in Norway where he is teaching mathemtics and didactics. He is also teaching mathematics and didactics at Bergen university college, and history of mathematics at the University of Bergen. His research interests are history of mathematics, and history of mathematics education.