The Solid Story

1
The Solid Story

• By
• Cindy Didawick
• August 6, 2003

2
Committee Members

• Dr. Loren Pitt
• Dr. Bill Haver
• Dr. Aimee Ellington
• Funded by The National Science Foundation

3
Science vs Philosophy Science was philosophical
because neither side could present evidence to
support its viewpoint. Modern science differs
from the approach of the ancient Greeks by its
reliance not only on logic but also on the
systematic gathering of facts by observation and
experimentation, and by the rigorous testing of
hypotheses. An Introduction to Physical Science
by James Shipman, Jerry Wilson and Aaron Todd
4
In the fourth century B.C., the Greek
philosopher Aristotle developed the idea that all
matter on the Earth is composed of four
elements earth, air, fire, and water. An
Introduction to Physical Science by James
Shipman, Jerry Wilson and Aaron Todd
5
The Solid History Plato thought the five
beautiful solids were a mathematical way of
describing these elements. He had no intention
of having these solids named after himself, but
wrote about them extensively hence the name
Platonic Solids. (Pythagoreans discovered the
tetrahedron, hexahedron and the dodecahedron.
Theaetetus is credited with the octahedron and
the icosahedron.)
6
History
h
Four elements and the universe Hexahedron
stands stable EARTH Octahedron rotates
freely AIR Tetrahedron light and
sharp FIRE Icosahedron largest
volume WATER Dodecahedron 12 zodiacs
UNIVERSE
7
Both Kepler and Plato were wrong with their
atomic theories. But, when we seek to see
patterns in nature through abstract patterns of
mathematics, we continue to make discoveries
today. Mathematics The Science of Patterns by
Keith Devlin
8
Facts

• All faces are identical regular polygons
• P,Q identifies each solid ( P the number of
  sides of each face and Q the number of faces
  that meet at the vertex)
• Each vertex sums to less than 360 degrees. (The
  figure would lie flat or tesselate if the sum
  360 degrees)
• Satisfy Eulers Formula (F V E 2)

9
Hexahedron or Cube
Facts 4,3 6 faces, 8 vertices, 12 edges Faces
are regular quadrilaterals (squares) Gold, Silver
and Salt Earth - stable Dual gt Octahedron
10
(No Transcript)
11
Octahedron
Facts 3,4 8 faces, 6 vertices, 12 edges Faces
are eguilateral triangles Diamond and
Fluorite Air Dual gt Cube
12
(No Transcript)
13
Tetrahedron
Facts 3,3 4 faces, 4 vertices, 6 edges Faces
are equilateral triangles Viruses and
Methane Fire light and sharp Dual gt Itself
14
(No Transcript)
15
Icosahedron
Facts 3,5 20 faces, 12 vertices, 30
edges Faces are eguilateral triangles Viruses Wat
er mobile, fluid, rolls easily Dual gt
Dodecahedron
16
(No Transcript)
17
Dodecahedron
Facts 5,3 Faces are regular pentagons 12
faces, 20 vertices, 30 edges Diamond and
Viruses Universe 12 zodiacs Dualgt Icosahedron
18
(No Transcript)
19
The great book of nature can only be read by
those who know the language in which it is
written. And this language is mathematics.
Galileo
20
Resourses
www.math.utah.edu http//home.teleport.com www.mat
hpages.com http//mathforum.org The Story of
Mathematics by Hy Ruchlis String, Straightedge,
and Shadow by Julia Diggins Mathematical Scandals
by Theoni Pappas Mathematics The Science of
Patterns by Keith Devlin