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

Origami - Math Problem Example For a dodecahedron, at least 3 different colors are required, as a dodecahedron cannot be properly colored in less than 3 colours. It is advisable to draw the planar graph of a a dodecahedron when planning the 3-edge coloring. "It is always quite puzzling to try to make use only 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 Hamilton who was a mathematician from Ireland, invented a puzzle 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. Hamilton's puzzle can be solved by beginning from any given city (i.e. any vertex) and traveling around the world from one city (vertex) to another. This entails that one moves along the edges of the dodecahedron in such a manner that each other city is touched only once before going back to the original vertex or starting point. This solution to Hamilton's 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 dodecahedron References J.A.Gallian (2006) Contemporary Abstract Algebra. Houghton R.A.Brualdi (2004) Introductory Combinatorics. Prentice Hall T.Hull (2006) Project Origami-Activities for Exploring Mathematics. A K Peters

Sapir-Whorf Hypothesis Essay Example | Topics and Well Written Essays - 1500 words

Sapir-Whorf Hypothesis - Essay Example There is the sense that the speaker’s development of language determines the way they experience the world and that there are connections to the individual’s identity that foundationally links it to the speaker -- anthropologist Michael Agar compares it to a prison. An example of this version occurs in the text when the author discusses his difficulty learning the Czech time system, as it differed from English in the way parts of the hour were described: in Czech, 9:45 is described as three-quarters of 10:00. He surmises that the Czech people might be more future oriented, indicating an deep, cognitive connection between linguistic culture and the Czech experience of the unfolding world. The ‘weak’ version of the hypothesis offers a less strict connection between the individual and their use of language, but retains the direct connection between the user’s cognitive interpretation of the world and their specific language. The ‘weak’ vers ion is demonstrated in the deictic discussions of the Guugu-Yimidhirr language in northeastern Australia.