Amazing Math: Introduction to Platonic Solids by Sunil Tanna PDF

By Sunil Tanna

ISBN-10: 150308485X

ISBN-13: 9781503084858

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

issues lined comprise:

  • What the Platonic solids are
  • The heritage of the invention of Platonic solids
  • The universal positive factors of all Platonic solids
  • The geometrical info of every Platonic strong
  • Examples of the place every one form of Platonic reliable happens in nature
  • How we all know there are just 5 sorts of Platonic stable (geometric facts)
  • A topological facts that there are just 5 kinds of Platonic sturdy
  • What are twin polyhedrons
  • What is the twin polyhedron for every of the Platonic solids
  • The relationships among every one Platonic reliable 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 outside sector of a Platonic sturdy
  • How to calculate the amount of a Platonic sturdy

additionally integrated is a quick advent to a few different fascinating varieties of polyhedra – prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra.

a few familiarity with uncomplicated trigonometry and intensely easy algebra (high college point) will let you get the main out of this e-book - yet which will make this ebook obtainable to as many of us as attainable, it does comprise a short recap on a few beneficial simple strategies from trigonometry.

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Extra info for Amazing Math: Introduction to Platonic Solids

Sample text

There also molecules which can be considered to be a distorted tetrahedron, for example, ammonia (NH3). In the case of ammonia, there is a central nitrogen atom, surrounded by 3 hydrogen atoms (each connected with a covalent bond), and also an additional lone pair of electrons (a pair of electrons which are not used for bonding). You can still imagine ammonia as a tetrahedron, provided you remember that one vertex of the tetrahedron is occupied by a lone pair of electrons rather than a hydrogen atom.

The adjacent is the side connecting the chosen angle (marked Θ in the diagram below) to the right angle. The opposite is the side which is opposite the chosen angle (marked Θ in the diagram below). The trigonometric functions are then defined: sine (often abbreviated to sin) is the ratio of the Opposite to the Hypotenuse. That is to say sin Θ = Opposite ÷ Hypotenuse cosine (often abbreviated to cos) is the ratio of the Adjacent to the Hypotenuse. That is to say cos Θ = Adjacent ÷ Hypotenuse tangent (often abbreviated to tan) is the ratio of the Opposite to the Adjacent.

The geometrical details of a regular hexahedron are: A regular hexahedron has 6 faces. Each face in a regular hexahedron has 4 edges – so is a 4-sided regular polygon, namely a square. There are 8 vertices in a regular hexahedron, each vertex being formed where 3 faces meet. There are 12 edges (formed whenever only 2 faces meet) in a regular hexahedron. The face angle (the angle at each vertex on each polygonal face) is 90°. The dihedral angle (the angle between two faces at an edge) is 90°. The vertex angle (the angle between edges at a vertex) is also 90°.

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Amazing Math: Introduction to Platonic Solids by Sunil Tanna

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