Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 Left Relatively Convex Subgroups
- 2 Groups with Context-free Co-word Problem and Embeddings into Thompson’s Group V
- 3 Limit Sets for Modules over Groups Acting on a CAT(0) Space
- 4 Ideal Structure of the C∗-algebra of R. Thompson’s group T
- 5 Local Similarity Groups with Context-free Co-word Problem
- 6 Compacta with Shapes of Finite Complexes: a Direct Approach to the Edwards–Geoghegan–Wall
- 7 The Horofunction Boundary of the Lamplighter Group L2 with the Diestel–Leader metric
- 8 Intrinsic Geometry of a Euclidean Simplex
- 9 Hyperbolic Dimension and Decomposition Complexity
- 10 Some Remarks on the Covering Groups of a Topological Group
- 11 The Σ-invariants of Thompson’s group F via Morse Theory
8 - Intrinsic Geometry of a Euclidean Simplex
Published online by Cambridge University Press: 27 August 2018
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 Left Relatively Convex Subgroups
- 2 Groups with Context-free Co-word Problem and Embeddings into Thompson’s Group V
- 3 Limit Sets for Modules over Groups Acting on a CAT(0) Space
- 4 Ideal Structure of the C∗-algebra of R. Thompson’s group T
- 5 Local Similarity Groups with Context-free Co-word Problem
- 6 Compacta with Shapes of Finite Complexes: a Direct Approach to the Edwards–Geoghegan–Wall
- 7 The Horofunction Boundary of the Lamplighter Group L2 with the Diestel–Leader metric
- 8 Intrinsic Geometry of a Euclidean Simplex
- 9 Hyperbolic Dimension and Decomposition Complexity
- 10 Some Remarks on the Covering Groups of a Topological Group
- 11 The Σ-invariants of Thompson’s group F via Morse Theory
Summary
We give a simple technique to compute the distance between two points in an n-dimensional Euclidean simplex, where the points are given in barycentric coordinates, using only the edge lengths of that simplex. We then use this technique to verify a few computations which will be used in subsequent papers. The most important application is a formula for intrinsically computing the volume of a Euclidean simplex, which is more efficient (and more natural) than any previously documented methods.
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- Chapter
- Information
- Topological Methods in Group Theory , pp. 135 - 145Publisher: Cambridge University PressPrint publication year: 2018
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