Origami Math Problem Example | Topics and Well Written Essays - 750 words

Origami - Math Problem ExampleFor a dodecahedron, at least 3 different twine are required, as a dodecahedron cannot be properly colored in less than 3 colours. It is better(predicate) to draw the planar graph of a a dodecahedron when planning the 3-edge coloring. It is always quite puzzling to exertion to make use tho 3 colors of paper with no two units of the same color touching. Each unit corresponds to an edge of the planar graph, so this is equivalent to a proper 3-edge-coloring of the polyhedron. (T.Hull, 2006)During the nineteenth century, Sir William rowan tree Hamilton who was a mathematician from Ireland, invented a fetch known as Around the World. The concept behind the puzzle was to label the vertices of a regular dodecahedron according to the names of various cities of the world. Hamiltons puzzle can be solved by inception from any given city (i.e. any vertex) and traveling around the world from genius city (vertex) to another. This entails that one moves along th e edges of the dodecahedron in such a manner that each other city is touched only once before going back to the authoritative vertex or starting point. This solution to Hamiltons puzzle is known as a Hamilton cycle/Hamilton circuit. Thus, a Hamilton circuit can be said to be a path in the dodecahedron which starts at a vertex, touches every other vertex, in the dodecahedron, and then returns to the original starting point without touching any single vertex two times.A Hamilton circuit in the planar graph of a dodecahedronReferencesJ.A.Gallian (2006) Contemporary Abstract Algebra. HoughtonR.A.Brualdi (2004) Introductory Combinatorics. Prentice Hall T.Hull (2006) Project Origami-Activities for Exploring Mathematics. A K Peters