Imaging geometry
The imaging geometry is the branch of geometry , the geometric figures studied. The invariants of the relevant images, that is to say those properties of geometric objects that remain unchanged when the relevant images are used, are characteristic of a certain class of geometric images . This view of geometry was propagated in particular by Felix Klein in his Erlangen program .
The mapping geometry includes, for example, the similarity maps (with the invariants path ratio and angle size ) or the congruence maps (with the invariants path length and angle size).
Mapping geometry in mathematics didactics
In mathematics didactics, imaging geometry or movement geometry denotes the didactic concept of operating geometry with the help of images and their properties, which is compared to the usual congruence geometry method according to Euclid.
In the Soviet Union , this approach was proposed by Andrei Kolmogorow together with set theory for a teaching reform and implemented from 1966 in a reform of mathematical teaching in schools under the name New Mathematics .
literature
- Heinrich Guggenheimer (1967) Plane Geometry and Its Groups , Holden-Day.
- Roger Evans Howe & William Barker (2007) Continuous Symmetry: From Euclid to Klein , American Mathematical Society, ISBN 978-0-8218-3900-3 .
- Robin Hartshorne (2011) Review of Continuous Symmetry , American Mathematical Monthly 118: 565-8.
- Roger Lyndon (1985) Groups and Geometry , # 101 London Mathematical Society Lecture Note Series, Cambridge University Press ISBN 0-521-31694-4 .
- PS Modenov and AS Parkhomenko (1965) Geometric Transformations , translated by Michael BP Slater, Academic Press .
- George E. Martin (1982) Transformation Geometry: An Introduction to Symmetry , Springer Verlag .
- Isaak Yaglom (1962) Geometric Transformations , Random House.
- Transformations teaching notes from Gatsby Charitable Foundation
- Kristin A. Camenga (NCTM's 2011 Annual Meeting & Exposition) - Transforming Geometric Proof with Reflections, Rotations and Translations.
- Nathalie Sinclair (2008) The History of the Geometry Curriculum in the United States , pp. 63-66.
- Zalman P. Usiskin and Arthur F. Coxford. A Transformation Approach to Tenth Grade Geometry, The Mathematics Teacher, Vol. 65, No. 1 (January 1972), pp . 21-30 .
- Zalman P. Usiskin. The Effects of Teaching Euclidean Geometry via Transformations on Student Achievement and Attitudes in Tenth-Grade Geometry, Journal for Research in Mathematics Education, Vol. 3, No. 4 (Nov. 1972), pp. 249-259.
- TO Kolmogorov. Геометрические преобразования в школьном курсе геометрии, Математика в школе, 1965, Nº 2, pages 24-29. (Geometric Transformations in a Geometry Course at School) (Russian)
- Peter Kirsche "Introduction to mapping geometry", series mathematik-abc for the teaching profession, Teubner 1998
- Hans Schupp "Abbildungsgeometrie", 4th edition Beltz 1974
Web links
- Georges Glaeser - The crisis of geometry teaching
- RS Millman - Kleinian transformation geometry, Amer. Math. Monthly 84 (1977)
- UNESCO - New trends in mathematics teaching, v.3, 1972 / page 8
- Barbara Zorin - Geometric Transformations in Middle School Mathematics Textbooks
- UNESCO - Studies in mathematics education. Teaching of geometry
- Peter Bender: Image geometry in the mathematics didactic discussion