Paige MacDonald and Michael Klug
Artists
Paige MacDonald and Michael Klug
Student of Mathematics
University of California, Berkeley
Berkeley, California, USA
Statement
This work displays a combination of two different pieces of mathematics - the Platonic solids and the Hopf fibration. The Ancient Greeks recognized that there are exactly five Platonic solids - the tetrahedron, hexahedron (cube), octahedron, dodecahedron, and icosahedron. The Hopf fibration, discovered by Heinz Hopf in 1931, gives a way of decomposing the 3-sphere into disjoint circles that are parameterized by points on a 2-sphere. For each platonic solid we chose the vertices of that solid on the 2-sphere and looked at the inverse image of those vertices under the Hopf fibration. We then used stereographic projection to project onto 3-dimensional space, and then projected the resulting image onto a plane.
Artworks
![Image for entry 'Tetrahedron Hopf'](/_next/image?url=https%3A%2F%2Fsubmit.bridgesmathart.org%2Frails%2Factive_storage%2Fblobs%2Fproxy%2FeyJfcmFpbHMiOnsiZGF0YSI6NjA3MCwicHVyIjoiYmxvYl9pZCJ9fQ%3D%3D--1607dea1f4e76a8cedca5582e1322c77c64e4763%2Ftetff2.jpg&w=1536&q=75)
Tetrahedron Hopf
60 x 75 cm
Digital Print
2016
![Image for entry 'Dodecahedron Hopf'](/_next/image?url=https%3A%2F%2Fsubmit.bridgesmathart.org%2Frails%2Factive_storage%2Fblobs%2Fproxy%2FeyJfcmFpbHMiOnsiZGF0YSI6NjA3MSwicHVyIjoiYmxvYl9pZCJ9fQ%3D%3D--21a0c512abf62d34f2b769efa09394174878135f%2Fdodff.jpg&w=1536&q=75)
Dodecahedron Hopf
60 x 75 cm
Digital Print
2016