HPSG2+2010 - Human Problem Solving General#2 Thought...

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Human Problem Solving 09/22/2010 General #2 : Thought problems for Tuesday September 28. Here are a few problems to think about for Thursday. You do not need to turn in anything, just think about them and form ideas that can be discussed in class. 1. There is an ‘interesting sense’ to the truth of the following paradoxical sounding statement. What is it and why does that sense make the statement true? Statement: You can not draw a perfect map of England in a London flat, but it is possible to do so in a New York City pad. 2. Suppose a,b, and c are numbers with c>0. Suppose a=b+c. I will now show the paradoxical result that a=b. What is wrong with my derivation? Step 1. a=b+c, c>0 Given Step 2. (a-b)a=(a-b)(b+c) Equal things multiplied by equal things are equal Step 3. a 2 -ab=ab+ac-b 2 -bc Multiply the terms out Step 4. a(a-b-c)=b(a-b-c) Transfer ac to the other side and factor Step 5. Therefore a=b Divide out (a-b-c) 3. You have 100 feet of fence. What is the largest (most area) rectangular garden that you can make with it? If you can make any shape, what shape gives the maximum garden area?
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  • Fall '10
  • WilliamH.BATCHELDER
  • Thumbtack, left thumbtack, right thumbtack, paradoxical sounding statement, forward/ backward length

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