Amazing Math: Introduction to Platonic Solids by Sunil Tanna

By Sunil Tanna

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

themes coated contain:

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

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

a few familiarity with simple trigonometry and intensely uncomplicated algebra (high college point) will let you get the main out of this booklet - yet so as to make this booklet available to as many of us as attainable, it does comprise a quick recap on a few valuable simple ideas from trigonometry.

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Extra info for Amazing Math: Introduction to Platonic Solids

Sample text

This is because they contain repeating units ("unit cells") based on arranging atoms in a cubic arrangement. Cubic pyrite crystals: There are in fact several different cubic arrangements (involving cubic-type unit cells) in which the atoms within crystals and minerals can be arranged, with different minerals adopting different arrangements depending on their composition and the relative sizes of the atoms involved. The three main varieties of cubic packing are: Primitive cubic (also known as simple cubic) Body-centered cubic Face-centered cubic (also known as cubic close-packed) Solid sodium chloride (NaCl) ionic crystal structure – chloride ions (Cl-) are shown in green, sodium ions (Na+) in blue.

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. That is to say tan Θ = Opposite ÷ Adjacent cosecant (often abbreviated to cosec) is the ratio of the Hypotenuse to the Opposite.

The geometrical details of a regular dodecahedron are: A regular dodecahedron has 12 faces. Each face in a regular dodecahedron has 5 edges – so is a 5-sided regular polygon, namely a regular pentagon. There are 30 vertices in a regular dodecahedron, each vertex being formed where 3 faces meet. There are 20 edges (formed whenever only 2 faces meet) in a regular dodecahedron. The face angle (the angle at each vertex on each polygonal face) is 108°. 57° (approximately). The vertex angle (the angle between edges at a vertex) is 108°.

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Categories: Geometry Topology