Check out my model of an icosahedron. I’ve been itching to construct one after reading about it in The Power of Limits. I finally found some time during the Christmas Holidays.
The icosahedron is one of the five regular solids discovered by Pythagoras and further explored by Plato, Kepler and many others. (Actually, there is ample evidence that they were well known to non-Greek cultures in times predating Pythagoras, but he is the first, as far as we know, to prove logically and mathematically that there are five and only five regular solids—no others are possible.) The icosahedron has twenty sides, each of which is an equilateral triangle. A glimpse from different angles reveals that it reverberates with both pentagonal and hexagonal harmonies. Most intriguingly, its internal core consists of three golden rectangles which intersect one another at right angles, and whose short sides touch upon opposing edges of the overall form.
For Plato and for the medieval alchemists and astrologists, each of the five regular solids was associated with one of the fundamental “elements” (earth, fire, air, water and ether or quintessence, the “fifth essence”) believed at that time to comprise the universe. The icosahedron was most often associated with water, though some of the lesser authorities assigned it as the representative of ether or quintessence (a role usually filled by the dodecahedron, or twelve-sided solid).
Monday, January 11, 2010
Topic: Geometry and Mathematics
Posted by Abrahamus at 8:00 AM