By Sunil Tanna
This e-book is a advisor to the five Platonic solids (regular tetrahedron, dice, common octahedron, average dodecahedron, and ordinary icosahedron). those solids are vital in arithmetic, in nature, and are the single five convex general polyhedra that exist.
themes lined contain:
- What the Platonic solids are
- The background of the invention of Platonic solids
- The universal positive factors of all Platonic solids
- The geometrical information of every Platonic reliable
- Examples of the place every one kind of Platonic stable happens in nature
- How we all know there are just 5 varieties of Platonic good (geometric facts)
- A topological evidence that there are just 5 forms of Platonic strong
- What are twin polyhedrons
- What is the twin polyhedron for every of the Platonic solids
- The relationships among every one Platonic stable and its twin polyhedron
- How to calculate angles in Platonic solids utilizing trigonometric formulae
- The dating among spheres and Platonic solids
- How to calculate the skin region of a Platonic stable
- How to calculate the quantity of a Platonic reliable
additionally incorporated is a short advent to a couple different fascinating forms of polyhedra – prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra.
a few familiarity with simple trigonometry and intensely simple algebra (high institution point) will let you get the main out of this e-book - yet as a way to make this booklet obtainable to as many folks as attainable, it does comprise a short recap on a few precious uncomplicated techniques from trigonometry.
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This e-book is a consultant to the five Platonic solids (regular tetrahedron, dice, typical octahedron, standard dodecahedron, and normal icosahedron). those solids are vital in arithmetic, in nature, and are the one five convex standard polyhedra that exist. issues lined comprise: What the Platonic solids are The heritage of the invention of Platonic solids the typical beneficial properties of all Platonic solids The geometrical info of every Platonic reliable Examples of the place each one form of Platonic stable happens in nature How we all know there are just 5 sorts of Platonic strong (geometric facts) A topological facts that there are just 5 forms of Platonic stable What are twin polyhedrons what's the twin polyhedron for every of the Platonic solids The relationships among every one Platonic reliable and its twin polyhedron how you can calculate angles in Platonic solids utilizing trigonometric formulae the connection among spheres and Platonic solids the best way to calculate the skin sector of a Platonic good easy methods to calculate the amount of a Platonic strong additionally integrated is a short advent to a few different attention-grabbing sorts of polyhedra – prisms, antiprisms, Kepler-Poinsot polyhedra, Archimedean solids, Catalan solids, Johnson solids, and deltahedra.
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Additional info for Amazing Math: Introduction to Platonic Solids
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. These shapes are not only important mathematically, but are also found in the natural world, and also have applications in science and technology.
The Euler characteristic of a shape/space, denoted by the Greek letter chi which has symbol χ, is a number which describes the shape/space regardless of how it might be bent or deformed by continuous deformations. A portrait of Leonhard Euler (April 15th, 1707 to September 18th, 1783) appears on this Swiss 10 Franc note. Euler was one of the greatest mathematicians in history, and it is after him that the Euler characteristic is named. The formula for χ is: where V is the number of vertices in the shape/space, E the number of edges, and F the number of faces.
None of Theaetetus' own writings have survived, but we know of him from one of Plato's dialogues about the nature of knowledge. The earliest surviving proof that there are only 5 types of Platonic solids comes from Euclid of Alexandria, a Greek mathematician who lived in Egypt and is sometimes known as the "Father of Geometry" because of his great contributions to this field. This proof appears in Euclid's treatise entitled Elements, which was written in about 300 BC. We don't know whether the original source of proof that appears in Elements, but it was most likely based on Theaetetus' work.
Amazing Math: Introduction to Platonic Solids by Sunil Tanna