## Amazing Math: Introduction to Platonic SolidsThis book is a guide to the 5 Platonic solids (regular tetrahedron, cube, regular octahedron, regular dodecahedron, and regular icosahedron). These solids are important in mathematics, in nature, and are the only 5 convex regular polyhedra that exist. Topics covered include: - What the Platonic solids are
- The history of the discovery of Platonic solids
- The common features of all Platonic solids
- The geometrical details of each Platonic solid
- Examples of where each type of Platonic solid occurs in nature
- How we know there are only five types of Platonic solid (geometric proof)
- A topological proof that there are only five types of Platonic solid
- What are dual polyhedrons
- What is the dual polyhedron for each of the Platonic solids
- The relationships between each Platonic solid and its dual polyhedron
- How to calculate angles in Platonic solids using trigonometric formulae
- The relationship between spheres and Platonic solids
- How to calculate the surface area of a Platonic solid
- How to calculate the volume of a Platonic solid
Some familiarity with basic trigonometry and very basic algebra (high school level) will allow you to get the most out of this book - but in order to make this book accessible to as many people as possible, it does include a brief recap on some necessary basic concepts from trigonometry. |

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