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The Solid Story

The Solid Story. By Cindy Didawick August 6, 2003. Committee Members. Dr. Loren Pitt Dr. Bill Haver Dr. Aimee Ellington Funded by The National Science Foundation. Science vs Philosophy:

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The Solid Story

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  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 Euler’s 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 > Octahedron

  10. Octahedron Facts: {3,4} 8 faces, 6 vertices, 12 edges Faces are eguilateral triangles Diamond and Fluorite “Air” Dual > Cube

  11. Tetrahedron Facts: {3,3} 4 faces, 4 vertices, 6 edges Faces are equilateral triangles Viruses and Methane “Fire” – light and sharp Dual > Itself

  12. Icosahedron Facts: {3,5} 20 faces, 12 vertices, 30 edges Faces are eguilateral triangles Viruses “Water” – mobile, fluid, rolls easily Dual > Dodecahedron

  13. Dodecahedron Facts: {5,3} Faces are regular pentagons 12 faces, 20 vertices, 30 edges Diamond and Viruses “Universe” – 12 zodiacs Dual> Icosahedron

  14. “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

  15. Resourses www.math.utah.edu http://home.teleport.com www.mathpages.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

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