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hi everyone Iamp;#39;m Parker Glen 80 and Iamp;#39;m going to talk about from colorings to fixed points so how we can use colorings of graphs to get fixed points in real analysis okay so this is a proof that could come up in a lot of different courses it could come up in C 32 which is graph theory and algorithms it could come up in C 27 which is topology or if you come up and see 44 were just coming to torques so it sort of could happen in a lot of different places what I like about this proof is that it gives us an algorithm so letamp;#39;s get into it okay so consider a string of beads okay so weamp;#39;re gonna color our beads red and blue okay and theyamp;#39;re going to impose that the first bead has to be blue and the other bead the last bead has to be red so weamp;#39;re going to call such a collection of beads well colored if the first feed is blue and the last bead is ready okay so now I want to draw your attention to a fact about well colored strings of beads if we look
