Chapter 4 questions

Chapter 4 questions - What does each possibility lead to?...

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Read the rest of Chapter 4, pages 161-187, and send in your answers to the following questions before 7 am Monday. 1. Which of the equivalent versions of Euclid's fifth postulate seems the most intuitively obvious to you? Why would that version be difficult to prove? To me the most obvious idea presented is the Triangle Area Property: The area of a triangle can be as large as we please. The only reason this property is hard to prove is because nothing can actually be proven and that a triangle with an infinite area is un-fathomable by the human brain, and therefore we cannot "please" the triangle to be as large as infinity. 2. What are Saccheri's three possibilities?
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Unformatted text preview: What does each possibility lead to? 1. there is exactly on parallel; 2. there are no parallels; 3. there is more than one parallel. 1. was Euclid's 5th, led to exactly one parallel; 2. led to a contradiction, there cannot be "no parallels" 3. led to many counterintuitives, but no contradiction, there may be more than one parallel. 3. In perspective geometry, what is a point at infinity? A point where parallel lines meet. 4. Why do we say a three -dimensional boat sailing on the ocean is moving in only two dimensions? Because the location of the boat need only be tracked by two parameters....
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This note was uploaded on 04/29/2008 for the course REL 100 taught by Professor Depends during the Spring '08 term at Augsburg.

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