platonic solids in nature
TRANSCRIPT
Platonic SolidsSixth Grade Geometry
Cube
Tetrahedron
Octahedron
Icosahedron
Dodecahedron
A History of Platonic Solids
• There are five regular polyhedra that were discovered by the ancient Greeks.
• The Pythagoreans knew of the tetrahedron, the cube, and the dodecahedron; the mathematician Theaetetus added the octahedron and the icosahedron.
These shapes are called the Platonic solids, after the ancient Greek philosopher Plato; Plato, who greatly respected Theaetetus' work, speculated that these five solids were the shapes of the fundamental components of the physical universe
Plato associated one solid with each of the four basic elements -- fire, earth, air, and water. He reserved the fifth for the heavens beyond the
stars and planets
Polyhedrons or Polyhedra
• A polyhedron is a solid formed by flat surfaces.• We constructed regular convex polyhedrons:– “regular” refers to the fact that every face, every edge
length, every facial angle, and every dihedral angle (angle between two faces) are equal to all the others that constitute the polyhedron.
– “convex” refers to the fact that all of the sides of the shapes are flat planes, i.e., they are not “concave”, or dented in.
Characteristics of Regular Convex Polyhedra
• Each face is congruent to all others• Each face is regular• Each face meets the others in exactly the
same way
Five Platonic Solids
Platonic Solids in Nature
PETUNIA
DODECAHEDRON
HERPES VIRUS
Icosahedron
Geodesic dome
Icosahedron
AMETRINE QUARTZ CRYSTAL
ICOSAHEDRON
Platonic Solid Quiz
• https://docs.google.com/forms/d/19uiDUri76QRNH_2V_U7vUvuTj87gzXgMKhOp8i8_7NY/viewform
Works CitedEarth Grids http://www.timstouse.com/EarthChanges/earthgrids.htm Web 19 April 2013
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