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Amazing Math: Introduction to Platonic Solids Amazing Math: Introduction to Platonic Solids

This 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 and nature, and the only types of 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
  • An introduction to some other interesting types of polyhedra - prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra.
Note: 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, I have included a brief recap on some necessary basic concepts from trigonometry (such as sine, cosine, radians, etc.).

This book is now available as both a printed book, and as an electronic book on Amazon Kindle!

For more information visit Sunil Tanna’s web page about Introduction to Platonic Solids


Paperback Book
eBook (Electronic Book) - Available for Kindle

This book has been specially prepared for use on the Kindle - including taking great care to ensure all math symbols, formulas, and calculations display correctly on the Kindle screen (many other math books do not display math symbols correctly). A color screen is recommended, but not essential - there are a couple of diagrams where the text refers to colors in the picture - but these should still be understandable even on a black and white screen.




 
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