Upload
ther
View
2.190
Download
0
Embed Size (px)
DESCRIPTION
Slide with some basic explanations
Citation preview
The Platonic Solids
Index of Contents
1. A brief review of some geometry concepts.2. The solids and their magic.3. 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 = 12Octa = 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!