module Pythagoras where

import Question

pythagoras :: WithHTML x CGI ()
pythagoras = do

  h2 $ text "More to do"

  p <#>If you still have some spare time, try the following a
           little more demanding exercises:</#>

  ul $ do

    li $ p <#>Define a function <tt>vectorLength</tt> that computes the
              length of a vector. Represent the vectors in a suitable
              way. (Maybe you can use two arguments of some numerical
              type to represent the vector?)</#>

    li $ p <#>Define a function (operator) <tt>+.</tt> that adds
              vectors. Does your function need a pair as result?
              Use <tt>(x, y)</tt> to construct a pair that contains
              <tt>x</tt> and <tt>y</tt>.</#>

    li $ p <#>Define a test that verifies that your vectors satisfy
              the triangle inequality rule. The triangle inequality states that
              the vector sum of two vectors never exceeds the total length of
              these two vectors.</#>

  p <#>In the next lecture you will see how the above can be done in a
           nicer way by defining a new type. Those of you who can't
           wait for the answer may take a peak at the end of the
           lecture notes.</#>