Chapter 5.1

Notes

Linguistic Mapping Exercises

Knowledge Checks

  1. Take \(D\) to be the disk of radius \(4\) with center at \((1,3)\). Find a path that parameterizes the boundary of \(D\) in the clockwise direction.
  2. Take \(R\) to be the rectangle with vertices \((4,3), (7,5), (3,11)\) and \((0,9)\). Find a piecewise linear function \(c\) that parameterizes the boundary of \(R\) and simulate the motion of a particle whose position at time \(t\) is \(c(t)\).
  3. Take \(R\) to be the rectangle with vertices \((4,3), (7,5), (3,11)\) and \((0,9)\). Describe \(R\) as the feasible set of inequalities.
  4. Take \(R\) to be the rectangle with ordered vertex set \((4,3), (7,5), (3,11)\) and \((0,9)\). Is \(R\) positively oriented?
  5. Take \(R\) to be the rectangle with ordered vertex set \((4,3), (7,5), (3,11)\) and \((0,9)\). Find a translation and rotation so that \((4,3)\) is moved to \((0,0)\) and one of the edges of \(R\) is on the \(x\)-axis.
  6. Take \(R\) to be the oriented triangle with ordered vertex set equal to \(((1,1),(4,2),(2,3))\). Find a continuous, piecewise linear parameterization for the boundary of \(R\), where the domain of the path is equal to \([0,4].\)

Practice Problems

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