Where did the name Platonic come from? These shapes were named after Plato, a Greek Philosopher. Plato did not discover these shapes, but they were still named after him because of the heavy importance he placed on these 5 perfect solids. Why are there only 5? The answer is very simple, because of the angles at the vertices. Math research project The 5 Platonic Solids Sides, Edges, Faces and Vertices A regular triangle has internal angles of 60°, so we can have:

3 triangles (3×60°=180°)

4 triangles (4×60°=240°)

or 5 triangles (5×60°=300°)

A square has internal angles of 90°, so there is only:3 squares (3×90°=270°)

A regular pentagon has internal angles of 108°, so there is only:

3 pentagons (3×108°=324°) The angles at the Vertex have to be less

than 360 degrees Well, why don't some of them work? # of sides each face has # of faces that meet degrees Does it work? 3

3

4

4

5

3

5

4

5

etc... 3

4

3

4

3

5

4

5

5

etc... 180

240

270

360

324

300

432

450

540

etc... (has to be uder 360 degrees) Euler's Formula Euler's Formula says: for any convex polyhedron (which includes the Platonic Solids) the Number of Faces plus the Number of Vertices (corner points) minus the Number of Edges always equals 2. So, does it work? 4+4-6=2 6+8-12=2 20+12-30=2 12+20-30=2 8+6-12=2 As you can see there are only 5 regular Solids that can work. If you disagree, good luck trying to prove it otherwise. :D My Scources

http://www.math.utah.edu/~pa/math/polyhedra/polyhedra.html

http://www.mathsisfun.com/geometry/platonic-solids-why-five.html

http://www.natures-word.com/sacred-geometry/the-platonic-solids/introduction-to-the-platonic-solids

Google images Thanks for watching!

### Present Remotely

Send the link below via email or IM

CopyPresent to your audience

Start remote presentation- Invited audience members
**will follow you**as you navigate and present - People invited to a presentation
**do not need a Prezi account** - This link expires
**10 minutes**after you close the presentation - A maximum of
**30 users**can follow your presentation - Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

### Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.

You can change this under Settings & Account at any time.

# The five platonic solids

No description

by

Tweet