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

Arlinghaus, Sandra Lach; Nystuen, John D.; Arlinghaus, S. L.

Arlinghaus, Sandra Lach; Nystuen, John D.; Arlinghaus, S. L.

1986

Citation:Arlinghaus, Sandra L. and Nystuen, John D. Mathematcal Geography and Global Art: The Mathematics of David Barr's "Four Corners Project." Ann Arbor: Institute of Mathematical Geography, Monograph Series, Monograph #1, Ann Arbor, 1986. 78 pages + http://hdl.handle.net/2027.42/58275

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.

Subject(s):Global Tetrahedral Sculpture, Mathematics of Sculpture

Description: 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.