The Platonic Solids
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The Platonic Solids

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Slide with some basic explanations

Slide with some basic explanations

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The Platonic Solids The Platonic Solids Presentation Transcript

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