Algebra VII - Combinatorial Group Theory, Applns to Geometry by A. Parshin,I. Shafarevich

By A. Parshin,I. Shafarevich

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What are the principles that are used to generate it? How might it be extended or varied? These questions are integral to appreciating the picture as a mathematical object. For example, if you see the picture as generated by a central interior pentagon with its edges extended in a Catherine-wheel manner, each by the same amount, then the outer pentagon is formed by joining up successive ends of the arms. The picture could be extended by doing the same thing to the outer pentagon: extending its edges to make another Catherine wheel.

How do those values relate to the five times table? How do they relate to the quickies in this chapter? Comment Most year 7 pupils quickly recognise that you can make 2 plus a multiple of 5, and suggest representations such as 2 + [something] × 5. The ‘something’ could be a box, a cloud (to represent a number that someone is thinking but as-yet-unknown to us), a cloud (to represent anything that someone might choose to think of), a word or short-form (number or numb) or a letter (such as n for number).

Similarly, the word imagine is taken to mean whatever inner sense(s) you experience, whether predominantly visual, aural or tactile. Sometimes one may be supplemented by the others; sometimes no one particular sense is dominant yet there is some ‘sense of ’ what is being talked about. The point is that most people have access to all senses, but some people have strongly developed preferences. Say What You See A diagram may ‘be worth a thousand words’, but it is not always easy to work out quite what those thousand words are!

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