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# The Platonic Solids

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### The Platonic Solids

1. 1. The Platonic Solids
2. 2. Index of Contents <ul><li>A brief review of some geometry concepts. </li></ul><ul><li>The solids and their magic. </li></ul><ul><li>A taste of their history. </li></ul>
3. 3. 1. A brief review of some geometry concepts <ul><li>Polygons: you know them very well! </li></ul><ul><li>Closed figure maded with segments. </li></ul><ul><li>Examples: triangles, quadrangles, pentagons, hexagons... </li></ul><ul><li>Regular polygons : every side has the same length. </li></ul>
4. 4. 1. A brief review of some geometry concepts <ul><li>Polyhedrons: we move on 3-D </li></ul><ul><li>Three-dimentional closed figure made with polygons. </li></ul><ul><li>Its parts are called: vertex, edges and faces. </li></ul><ul><li>Prisms and Pyramids are polyhedrons. </li></ul>
5. 5. 2. The platonic solids and their magic <ul><li>There is an unlimited number of different polyhedrons. </li></ul><ul><li>But...how many polyhedrons can we built on condition that: </li></ul><ul><li>we use only one kind of regular polygon </li></ul><ul><li>and </li></ul><ul><li>we must have the same number of edges in each vertex ? </li></ul><ul><li>Only the 5 platonic sòlids! </li></ul>
6. 6. 2. The platonic solids and their magic <ul><li>Here you have them : Tetrahedron, Hexahedron/Cube, Octahedron, Dodecahedron, Icosahedrom </li></ul><ul><li>Tetra = 4 Dodeca = 12 </li></ul><ul><li>Octa = 8 Icosa = 20 </li></ul><ul><li>Hexa = 6 Hedron = Face </li></ul>
7. 7. 2. The platonic solids and their magic <ul><li>It’s interesting to note that: </li></ul><ul><li>Because of their symmetry , they all can include and be included in a sphere. </li></ul><ul><li>They all 5 carry out Euler’s Formula </li></ul><ul><li>Vertex – Edges + Faces = 2 </li></ul>
8. 8. 3. A taste of their history <ul><li>They have been known since antiquity. </li></ul><ul><li>Carved stone balls from Scotland (400 aC) </li></ul><ul><li>Plato wrote about them in the Timeus (360 bC) </li></ul>
9. 9. 3. A taste of their history <ul><li>Ancient Greeks connected them with the four classical elements </li></ul><ul><li>and the Universe/Divinity . </li></ul>
10. 10. 3. A taste of their history <ul><li>In the 16th century, Kepler tried to link them with the 5 known planets but later he had to give up the idea. </li></ul>
11. 11. 3. A taste of their history <ul><li>Finally, artists of all time have been fascinated by the perfection of their shapes: </li></ul><ul><li>Da Vinci Dürer </li></ul>
12. 12. 3. A taste of their history <ul><li>Escher Dalí </li></ul>
13. 13. Epilogue <ul><li>I hope you have enjoyed the speech and I encourage you to look for the platonic solids wherever you go!!! </li></ul><ul><li>Thank You! </li></ul>