Amazing Math: Introduction to Platonic Solids by Sunil Tanna

By Sunil Tanna

This publication is a advisor to the five Platonic solids (regular tetrahedron, dice, common octahedron, standard dodecahedron, and normal icosahedron). those solids are very important in arithmetic, in nature, and are the one five convex common polyhedra that exist.

issues lined comprise:

  • What the Platonic solids are
  • The heritage of the invention of Platonic solids
  • The universal good points of all Platonic solids
  • The geometrical information of every Platonic stable
  • Examples of the place each one kind of Platonic stable happens in nature
  • How we all know there are just 5 varieties of Platonic sturdy (geometric facts)
  • A topological facts that there are just 5 forms of Platonic good
  • What are twin polyhedrons
  • What is the twin polyhedron for every of the Platonic solids
  • The relationships among each one Platonic stable and its twin polyhedron
  • How to calculate angles in Platonic solids utilizing trigonometric formulae
  • The courting among spheres and Platonic solids
  • How to calculate the skin region of a Platonic stable
  • How to calculate the amount of a Platonic good

additionally integrated is a short advent to a couple different attention-grabbing sorts of polyhedra – prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra.

a few familiarity with simple trigonometry and intensely easy algebra (high tuition point) will let you get the main out of this e-book - yet in an effort to make this booklet obtainable to as many folks as attainable, it does comprise a quick recap on a few important simple thoughts from trigonometry.

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Extra resources for Amazing Math: Introduction to Platonic Solids

Example text

A regular polygon is one where all the line segments are of equal length, and all the angles between line segments where they meet at each vertex (plural: vertices) are equal. and so on A polyhedron (plural: polyhedra or polyhedrons) is a 3-dimensional shape made from joining polygons together, with the polygons serving as the faces of the polyhedron. and so on – there are many other types of polyhedra! A regular polyhedron is one which is made of congruent (all the same size/shape, although mirror images are allowed) regular polygons assembled in the same way around each vertex (corner).

Com/math Introduction For some time now, I have been tutoring both adults and children in math and science. As a result, I have discovered that many people of all ages have a latent interest (and talent) in mathematics that is somehow never got fully awoken while in school. com). Most of my books are intended to teach specific topics and techniques, but I have also written others intended to awaken a student's interest in these subjects and broaden their horizons. This book is about a fascinating mathematical topic – Platonic solids – which are a particular kind of 3-dimensional shapes.

The geometrical details of a regular octahedron are: A regular octahedron has 8 faces. Each face in a regular octahedron has 3 edges – so is a 3-sided regular polygon, namely an equilateral triangle. There are 6 vertices in a regular octahedron, each vertex being formed where 4 faces meet. There are 12 edges (formed whenever only 2 faces meet) in a regular octahedron. The face angle (the angle at each vertex on each polygonal face) is 60°. 47° (approximately). The vertex angle (the angle between edges at a vertex) is 60° for edges which are part of the same face, and 90° for edges which are not.

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