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

• Main Authors: Arlinghaus, Sandra Lach, Nystuen, John D.
• Other Authors: Adjunct Professor of Mathematical Geography and Population-Environment Dynamics, School of Natural Resources and Environment, Professor of Urban Planning and Geography, Taubman College of Architecture and Urban Planning, Ann Arbor
• Format: Book
• Language: English
• Published: Institute of Mathematical Geography (printing by Michigan Document Services) 1986
• Subjects: Global Tetrahedral Sculpture; Mathematics of Sculpture; Geography and Maps; Social Sciences; Greenland
• Online Access: https://hdl.handle.net/2027.42/58275

This monograph contains Nystuen's calculations, actually used by Barr to position his abstract tetrahedral sculpture within the earth. Placement of the sculpture vertices in Easter Island, South Africa, Greenland, and Indonesia was chronicled in film by The Archives of American Art for The Smithsonian Institution. In addition to the archival material, this monograph also contains Arlinghaus's solutions to broader theoretical questions--was Barr's choice of a tetrahedron unique within his initial constraints, and, within the set of Platonic solids? The monograph includes a Preface by sculptor David Barr. 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. http://deepblue.lib.umich.edu/bitstream/2027.42/58275/2/Monograph01.pdf