Topic
Absolute geometry
About: Absolute geometry is a research topic. Over the lifetime, 855 publications have been published within this topic receiving 24201 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Mar 1976
3,561 citations
Book•
1 Jan 1976Abstract: Part I. Integral Geometry in the Plane: 1. Convex sets in the plane 2. Sets of points and Poisson processes in the plane 3. Sets of lines in the plane 4. Pairs of points and pairs of lines 5. Sets of strips in the plane 6. The group of motions in the plane: kinematic density 7. Fundamental formulas of Poincare and Blaschke 8. Lattices of figures Part II. General Integral Geometry: 9. Differential forms and Lie groups 10. Density and measure in homogenous spaces 11. The affine groups 12. The group of motions in En Part III. Integral Geometry in En: 13. Convex sets in En 14. Linear subspaces, convex sets and compact manifolds 15. The kinematic density in En 16. Geometric and statistical applications: stereology Part IV. Integral Geometry in Spaces of Constant Curvature: 17. Noneuclidean integral geometry 18. Crofton's formulas and the kinematic fundamental formula in noneuclidean spaces 19. Integral geometry and foliated spaces: trends in integral geometry.
2,158 citations
Book•
1 Jan 1969
TL;DR: In this paper, the authors describe the topology of surfaces in the Euclidean plane, including the Golden Section and Phyllotaxis, as well as the five Platonic solids.
Abstract: Triangles. Regular Polygons. Isometry in the Euclidean Plane. Two--Dimensional Crystallography. Similarity in the Euclidean Plane. Circles and Spheres. Isometry and Similarity in Euclidean Space. Coordinates. Complex Numbers. The Five Platonic Solids. The Golden Section and Phyllotaxis. Ordered Geometry. Affine Geometry. Projective Geometry. Absolute Geometry. Hyperbolic Geometry. Differential Geometry of Curves. The Tensor Notation. Differential Geometry of Surfaces. Geodesics. Topology of Surfaces. Four--Dimensional Geometry. Tables. References. Answers to Exercises. Index.
1,833 citations
Book•
21 Oct 2008
TL;DR: This chapter discusses the foundations of Stochastic Geometry, as well as some Geometric Probability Problems, and some of the facts from Convex Geometry.
Abstract: Foundations of Stochastic Geometry.- Prolog.- Random Closed Sets.- Point Processes.- Geometric Models.- Integral Geometry.- Averaging with Invariant Measures.- Extended Concepts of Integral Geometry.- Integral Geometric Transformations.- Selected Topics from Stochastic Geometry.- Some Geometric Probability Problems.- Mean Values for Random Sets.- Random Mosaics.- Non-stationary Models.- Facts from General Topology.- Invariant Measures.- Facts from Convex Geometry.
1,168 citations
Book•
24 Nov 1995
TL;DR: In this article, the authors introduce differential geometry, non-commutative geometry, vector bundles, cyclic homology, and extensions of space-time, and show how these can be combined.
Abstract: 1. Introduction 2. Differential geometry 3. Matrix geometry 4. Non-commutative geometry 5. Vector bundles 6. Cyclic homology 7. Modifications of space-time 8. Extensions of space-time.
880 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 2 |
| 2024 | 5 |
| 2023 | 9 |
| 2022 | 13 |
| 2021 | 5 |
| 2020 | 1 |