Introduction to the Platonic Solids

Welcome to another course on hands on maths, which means that I believe you learn more by making things and doing things than you do by listening to a teacher. Today’s course is on platonic solids. Now there are five platonic solids. And what are you going to do in this course? Well, the first thing is you’re going to make a model like this. And you’ll see here it’s a dodecahedron and the word universe on it more about that later. But as Open the dodecahedron and you’ll see there’s a cube inscribed in it. And the first thing to note is how neatly that cube inscribed inside the dodecahedron. Next, I’m going to take out the cube. Now inside the cube, there’s a tetrahedron. And again, note how neatly there’s tetrahedron inscribed in the cube. I’ll take it out inside the tetrahedron, there is an octahedron and it’s in a special position. And that’s for platonic solids. Now there’s one more and that is the icosahedron. And here it is sitting Inside the octahedron so that’s the five platonic solids later on PDF worksheets which you cut out. And then you can put them together with sticky type. The Greeks thought these platonic solids were very important. In fact, I thought they were perfect. And they equated the platonic solids to things in nature, trying to understand nature. So we’ll have a look at the history of platonic solids. I want to compare them to the archimedean solids. I’ll have a definition of platonic solids and also a lecture on why there are only five platonic solids. There’s also a worksheet for you to download. And all the calculations can be done on this single worksheet which is only two pages edges. I’ll give you some formulas on the worksheet. And what is that for? Well, we’re going to compare the volumes and surface areas of the model that we make. And I’m going to do this in the simplest possible way. I’m going to make the cube one. So as a volume, this is obviously one cubic unit. As an area, it’s six square units. And then we’ll see how the others compare to this cube. Who is is for at lower secondary level. Students usually study volumes and surface areas. Also, teachers at that level might find it convenient to download the PDF worksheets and photocopy the models and their students can make them. The worksheet can be printed back to back in black and white. In the next lecture, we’ll look at the history of the platonic solids. So I hope to see you then