worksheet3 - A = 1 2 3(50 points Generalize the results...

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MA 1002 Worksheet 3 Due Date: Seotember 30, 2009 Print Name: Signature: ID #: Instructor/Section: Instructions: Explain each step using the conventions from class. Please mark solutions clearly. You will not receive full credit for a correct answer without explanation. 1. (25 points) Find the area of the polygonal shape from class using Pick’s theorem. 2. (25 points) Use Pick’s theorem to show that any triangle whose vertices have integer coordinates and which does not contain lattice points in its interior has area
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Unformatted text preview: A = 1 2 . 3. (50 points) Generalize the results from class and ±nd similar estimates for ∑ N n =1 r 3 ( n ) by counting the grid points in the sphere of radius √ N . Here, r 3 ( n ) counts the number of ways to write n as a sum of 3 squares. 4. (extra) Find a convincing argument that every simple closed polygon can be cut into triangles by adding a sequence of straight lines between two vertices....
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