Reading Questions #10

Reading Questions #10 - Y and Z symmetries are...

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Read pages 189-205 and send in the answers to these questions before 7 am on Monday, November 12. 1. What does the author mean by "the mathematics of beauty"? In other words, what exactly is this chapter about? This chapter is about the aesthetics of Geometry, such as symmetries and transformations. 2. What is condition G4? Give a specific example of how a symmetry group can fail to satisfy this condition. Condition G4 is "For all x and y in G, x * y = y * x". In the Equilateral Triangle group, x * y = w, and y * x = v. This is because the X
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Unformatted text preview: Y and Z symmetries are self-inversisive. 3. Why did Galois create groups? What problem was he trying to solve? He created groups because he found that he could use multiple simpler equations to solve more complex formulas, mostly for Galois, the Quadratic formula. 4. What is a lattice? What is a lattice packing? "... a lattice is a collection of points arranged at the vertices of a regular, two-dimensional grid." Lattice packing is where a series of disks are put in such an order that CENTERS of their form, form a lattice....
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