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Hands-on Maths – The Platonic Solids (using a model)

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DESCRIPTION of  the COURSE

In this course, you’ll learn all about Platonic Solids, and you’ll do it by making a model.   This is easy since I supply you with PDF worksheets so you can cut out the outlines, and then put the model together with sticky tape. Having seen how the Platonic Solids inscribe inside one another, we will then calculate and compare their volumes and surface areas …  there is also a downloadable worksheet for this.

The Platonic Solids often come up in Maths tests and problems, and having a good understanding of them, means you will recognize them and find solutions quickly.      They are also a thing of wonder and beauty.     There are only five, and they have been known about since the time of Plato in ancient Greece, or even longer.  They were often seen as being key to understanding nature, be that the makeup of the world around us, of the orbits of the planets, or whatever.      Nevertheless, this is a Maths course, and I’ll show you how interesting mathematically they are.

What you’ll learn :

The names of the 5 Platonic Solids

The history of the Platonic Solids

A Definition and comparison to the Archimedean Solids

Why there are only 5 Platonic Solids

Making a paper model of Platonic Solids(which fit inside one another)

The nets of the Platonic Solids

Vertices, edges, sides and Euler’s formula

Volumes of Platonic Solids (a comparison)

Duality in Platonic Solids

Surface Areas of Platonic Solids  (a comparison)

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PRE-REQUISITES for the course

Students need to be able to handle square roots in formulas, and to enter square roots in a calculator for more complicated formulas.   These kind of problems are usually taught at the Lower Secondary Level.

Also, for the model, you’ll need to print out the nets, cut them out with scissors and put them together with sticky tape. There is also a 2 page worksheet to print out.   (It can be printed back to back in black and white)

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Introduction

1
Introduction

Background to The Platonic Solids

1
The History of The Platonic Solids
2
Definition and comparison to The Archimedean Solids
3
Only 5 Platonic Solids

The model of The Platonic Solids

1
Making the model
2
Nets of The Platonic Solids
3
Table of Faces
4
Side Lengths
5
Volumes (a comparison)
6
Duality
7
Surface Areas (a comparison)

Conclusion

1
Conclusion
5
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Duration: 1 hr. 13 min.
Lectures: 12
Video: 1 hr. 13 min
Level: Intermediate