In Perfect Shape The Platonic Solids

Going Greek?

The Greeks were very fond of symmetry Art Architecture MATH!!!

The most symmetric polygons are the regular ones Polygons with all sides and all angles congruent

Let’s dig a little bit deeper into what we want to convey here…

But to do this…we gotta know the facts…

Fact of Geometry: There are only a few regular polyhedra that exist! (Contrast to regular polygons which can have any number of sides.)

Five different types of polyhedra

Tetrahedron: 4 faces (triangles)

Hexahedron: 6 faces (squares)

Octahedron: 8 faces (triangles)

Dodecahedron: 12 faces (pentagons)

Icosahedron: 20 faces (triangles)

Hey Mike… I’m puzzled….why are there only five regular polyhedra?

Don’t be a pinhead…IT’S SIMPLE!!!!

Think about it this way A point or “peak” is formed by at least three polygonal faces that meet at any vertex of the polyhedron Since the polyhedron is regular, the situation at any vertex is the same as at any other. To make a peak, the sum of all the face angles at the vertex must be less that 360 degrees. If they add up to 360 degrees, they would make a flat surface. Since all the faces are congruent, the angle sum at a vertex must be divided up equally among them.

Justin….Let’s get our groove on with a little…..Earth Wind and Fire

Earth, Air, Water, and Fire Earth (Hexahedron) Air (Octahedron) Water (Icosahedron) Fire (Tetrahedron)

The Fifth Element

If interested in playing… an.htmlhttp:// an.html

Uses/Occurrences Dice: Crystal structures in nature. In meteorology and climatology, global numerical models of atmospheric flow are of increasing interest which employ grids that are based on an icosahedron (refined by triangulation) instead of the more commonly used longitude/latitude grid. This has the advantage of evenly distributed spatial resolution without singularities (i.e. the poles) at the expense of somewhat greater numerical difficulty. (Wikipedia)meteorologyclimatologytriangulationlongitudelatitudesingularitiespoles

Archimedean Solids Truncated Platonic Solids trplato.html The others archimed.html

Time Line ~ 400 BCE The Greeks: Plato and Platonic Solids ~250 BCE Archimedes and Archimedean Solids ~ ’s AD Renaissance: Rediscovery of Archimedean Solids ~1600 AD Kepler and Planetary Motion Today: Games, molecular structure, modeling

Works Cited Appel, Rudiger. 3Quarks-GIF Animations-Platonic Solids. 21 May Nov Berlinghoff, William, and Fernando Gouvea. Math Through The Ages: A Gentle History for Teachers and Others. Farmington: Oxen House Publishers, Google Image Search Google. 21 Nov Greaves, David. "What do viruses look like?." My Virion Home Page. 1 Jul Nov O'Connor, Aidrian. "Musings On Sacred Geometry." Nature's Word Nov "The Fifth Element Pictures." The MovieWeb Movie VAult. MovieWeb. 21 Nov