Geometry - Intuition and Concepts

- Incidence: Projective geometry 

- Parallelism: Affine geometry 

- Angle: Conformal Geometry 

- Distance: Metric Geometry 

- Curvature: Differential Geometry 

- Angle as distance measure: Spherical and Hyperbolic Geometry 

- Symmetry: Mapping Geometry.

The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions.

This book is a translation of the original German 1 ^st edition  Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.