Amazing Math: Introduction to Platonic Solids

Front Cover
CreateSpace Independent Publishing Platform, Oct 26, 2014 - 82 pages
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, 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
Also included is a brief introduction to some other interesting types of polyhedra - prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra.

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.

What people are saying - Write a review

We haven't found any reviews in the usual places.

About the author (2014)

Sunil Tanna is an author, software developer, and tutor (math and science). He writes... My first real memory of reading a book was when I was five, in infants school. The teacher was conducting a very detailed and rather slow lesson on how to tell the time. I already knew how to tell the time, or at least I thought I did, and I was bored. The whole class was sitting on a mat, and I happened to be sitting near the back, next to a bookshelf. I took a book off the shelf about a group of school children who investigated, and eventually solved, a smuggling mystery. Completely absorbed, I sat quietly reading to myself. I don't think it was a huge book, it couldn't have been, but I amazed myself by managing to read the entire book cover to cover. Just as I turned the last page, I suddenly realised that the lesson was coming to an end. I remember worrying that I might have missed some vital new detail of telling the time that perhaps the teacher had slipped in during the second half of the lesson. Somehow however I survived. I've had a love of books ever since, although nowadays I generally try to choose more opportune moments to read them. As a writer, I hope to write about both my personal experiences, and the things that interest me most. Since I have quite an eclectic range of interests, you can expect a diverse range of books from me in future.

Bibliographic information