Mathematical Geography and Global Art: The Mathematics of David Barr's "Four Corners Project."

Abstract

Table of Contents: Introduction | Four Corner Sites for the Tetrahedron Sculpture (Location of the Tetrahedron in a Sphere (In the Unit Sphere; In the Earth); Location of the Tetrahedron Vertices in Earth-Coordinates; More Efficient Use of this Approach to Barr's Problem; Determination of All Other Tetrahedra with One Vertex at Easter Island; Problems in Locational Precision Arising from the Assumed Sphericity of the Earth) | Extension of Barr's Problem to the Set of Platonic Solids (The Tetrahedron: {p,q} = {3,3}; The Cube: {p,q} = {4,3}; The Octahedron: {p,q} = {3,4}; The Dodecahedron: {p,q} = {5,3}; The Icosahedron: {p,q} = {3,5}; Table 3.1--Measurements Associated with Platonic Solids) | Uniqueness Questions (Generalization of Barr's Problem; Uniqueness Theorems) | Appendix A: Some Solid Geometry | Appendix B: Some Linear Algebra | Appendix C: Terrae Antipodum: Antipodal Landmass Map.