Information about The Platonic Solids

Published on April 23, 2008

Author: ther

Source: slideshare.net

Slide with some basic explanations

Index of Contents A brief review of some geometry concepts. The solids and their magic. A taste of their history.

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.

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.

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!

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

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

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)

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 .

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.

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

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

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!

I hope you have enjoyed the speech and I encourage you to look for the platonic solids wherever you go!!!

Thank You!

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